Job hopping is potentially a problem in getting into a PhD program. The fear of admissions, obviously, would be that your lack of commitment to one thing will show up again in your studies, and you will tire of this quickly, too.
However, it may be less of a problem here than in looking for new employment in industry. Some reasons:
- You are making a category shift, and as such all of your previous jobs may be seen as "one thing", and you are now switching to a completely different thing.
- There is quite a bit of anti-industry bias in some parts of academia. Therefore people considering your application might be more sympathetic to your work history. They might think "of course this person couldn't make it in the soulless, evil corporate world, but they will flourish in the academy." (Of course this is a bit of a caricature, but you get the idea).
- You are more likely to have a chance to tell your story. As discussed in the linked question, a "job hopper" may have their CV rejected well before they get to interview, having no chance to explain the circumstances. But when applying for a PhD, it is quite likely you will get far enough to have some personal interaction and explain your circumstances.
- They may be making less of a commitment to you than an employer would be. Particularly if you are looking at unfunded PhDs, they may be more willing to take you on, even if they think you are a risk, since you are paying them (not the other way around).
What should you do about it?
- Contact some professors at programs you are interested in. Share your story and interest in graduate study. This personal connection may help your chances as an applicant, and you can also get advice from them that will help determine whether (and where) you have a chance of success.
- Work hard on your personal statement. It should demonstrate clearly why you want to do a PhD, how you arrived at this conclusion, and show some commitment to this as your direction in life.
- If going directly into a PhD program doesn't seem feasible, consider alternative options. A master's program would be a lot easier to get into, and you can often then transfer into a PhD once there. Or, consider employment at an academic institution (such as work as a research assistant) where you can build up some recent academic experience while also making connections that will help you gain admission.