I would like to study for a PhD and hopefully become a researcher. There is nothing I can think of that I would like to do with my life more. However, my social and communication abilities are bad. They are bad beyond the point where it could be dismissed as me being a 'quirky professor'. People assume that if you want to go into academia, you want to teach. However, I don't think I could do it. I have Asperger syndrome, so there's a limit to how much I can improve my social skills. No matter how much I try to be 'normal', it doesn't work and it's massively draining, to the extent that I find myself struggling to do basic tasks because I get burnt out. There are staff at my university who seem to like me, so it's not as though it's impossible for me to form positive relationships with people in academia, but that's very different to being able to teach classes. Is there any point in me trying to pursue an academic career? Can I focus on research and do minimal or no teaching? I know that there are autistic people in academia, and that I'm pretty 'high-functioning' for an autistic person (i.e. I have it easier than a lot of autistic people, even though I do struggle a lot), but I don't want to set myself up to fail.
Staying at the university, i.e., eventually becoming a professor, will be hard / impossible without teaching. There are, however, research facilities that are usually financed half by industrial projects and half by funding from the state. If you get a job in one of these, you will have to aquire money by getting research projects accepted, and are then free to do research without any teaching obligations. Note that your contract there will probably never be any longer than 2-3 years at once. I will then hopefully be refreshed, but you will not have a lot of stability.
The main question may be whether you think you can do your PhD. That involves giving several presentations (at conferences and during your defense), a rather high level of stress tolerance, and probably occasional preassure from your advisor, especially during the last year.
I had a colleague who might have a slight form of Asperger, and he quit about one year before finishing his PhD, because it got to overwhelming. But there were several factors involved there, including him not being happy with the direction his research was going. So that might have nothing to say!
I have Asperger Syndrome as well, and I have thought about this question before.
Can I focus on research and do minimal or no teaching?
You are very unlikely to find a permanent position at university that does not include teaching. Some people stack postdoc upon postdoc spending decades on time-limited contracts that do not involve teaching. By "postdoc" here I do not mean a literal postdoc, but any research funded position for a period of typically anything between 6 months and 4 years. Some PIs are good at finding funding and will try to keep postdocs already working for them before advertising externally; in this case, you might be able to remain for decades. The catch is: you'll never have job security and you might stagnate in career development (including salary).
You may be able to find a permanent research position at at national or supranational institute, but again, this might come at a price. You might not have the academic freedom that you have at university; in some positions, you would essentially research the topic that you are told to. Your research will likely be applied; most likely no blue-sky science, although it does depend on the institute. You might not have time to write papers, but rather be delivering products and associated reports. Perhaps one should rather call it development than research. One place where such happens is within the ground segment of meteorological satellites. Such applications may or may not exist within your field, but changing fields is possible and probably easier when moving into development/applications as the "return on investment" on training a new arrival is larger when the expectation is that the new arrival stays for a long time (for example, the Met Office in the UK regularly advertises positions for which no prior knowledge of atmospheric science or meteorology is required).
The reason for this is: permanent money is given to stuff that funders consider useful or stable. Teaching is pretty secure; although student levels fluctuate, there will be a need to teach Gauss law today and this need will certainly still exist in 10, 20, 30, or 40 years. Applied research/development at govenment institutes may also be pretty secure; the next generation of meteorological satellites in Europe is planned until 2043. A calibration develment expert for one of those instruments is in a pretty good position to have long-term job security.
Although not to a pathological level, my social skills are fairly poor. What I can comment, after 30 years in academia, is that they have hurt my research career more than they have hurt my teaching.
To expand, as requested by Gerrit:
as for my research, my feeling is that there have been many lost many opportunities because of not being able to get close to people at conferences, visits, etc. I see people with similar talent compared to mine, that get way further because they know how to connect.
In my teaching, had I been able to get to my students better, their experience would have possibly been more satisfactory. But it is not clear that they would have learned more, as my outcomes are similar to other profs.
Contrary to what other answers are suggesting, there exist some countries which offer permanent research positions that do not feature any teaching and yet give very high freedom to researchers. For instance, in France, we have CNRS positions, which have no teaching and are rumored to offer essentially the highest level of academic freedom you could think of. There are other such positions in France, for instance at Inria in computer science. I think this model also exists in other countries.
The catch is that (in France) these positions are not very well paid (by international standards), and they are extremely competitive (much more so than standard university positions), in particular because there are many people who are interested in positions without teaching! Given the very high level, I would think it unwise to do a PhD and have such positions as your only goal. Yet, the possibility exists.
As other answers have pointed out, however, research does involve giving oral presentations of your work, which are very much like teaching; and it also requires stress tolerance, social interactions, etc. So it's not the case that these skills are just useful for teaching. Last, keep in mind that, when applying to academic positions, you need to pass an oral interview, which serves (among other purposes) to evaluate your communication skills.
Even research-only positions require good academic communication skills, and sufficient ability to work well in teams with others. But these are different things from the social skills needed in order to be comfortable in less formal social settings. If you want it enough, and have the toughness and ability to do research well, I bet you can find a way to handle what is needed, even for teaching positions.
My informal impression is that academia is full of professors who do fine in that setting, but simply do not have the intuitive social skills to (say) sell used cars for a living. Of course, there are some professors who are just great at everything, including social skills. But also many who do some things exceptionally well and others no better than just OK.
You should simply go forward with your ambition and avoid overthinking the matter. Yes, as pointed out by others, it would be difficult to avoid teaching, and social skills may be even more essential in research collaborations than in teaching. But everyone has their strengths and weaknesses (yours may simply have a name which tends to be on everyone's lips), and it is just impossible to predict the outcome, in absolute or relative terms (what's your plan B?). I've encountered people with noticeably autistic traits who were working and teaching in academia, and I'm quite certain that their outcome there was better than it otherwise might have been. Also, I'd avoid thinking that you can't improve substantially. Around 15% of children diagnosed with AS do not even meet the diagnostic criteria in adulthood. You should just give the project your best shot, and if it does not work out, don't think it as a failure. Think it as an experiment.
In the United States it's actually a huge issue where we've create a permanent postdoctoral fellow position, where is basically incredibly unlikely to get a professorship, and all these people do is do research. It's extremely common in biomedical science. You need a PhD though to do actual research. You can be a lab tech with some independence with just a M.S. but the pay may be a bit lower ,you are basically running someone else's experiments though.