It is well-known that LinkedIn is used by scholars too, but I think that the business-friendly structure of your profile-page makes it markedly less suitable for academic purposes. Is there a specifically academic website that includes the same characteristics as LinkedIn plus the possibility to add some more scholarly elements in your profile?
ResearchGate is more academic. It allows you to add your research publications, not just papers. It also has a stackexchange like section and a Jobs section, that features listings to research and advanced positions (PHD, Post-Doc) in academic institutions and in business.
As @StephanKolassa noted you should scout Research Gate before joining (follow the link in his comment), as any other alternative.
You could look at the aggregator/identifier system ORCID. I strongly recommend ORCID if you apply for US federal grants, as the writing is on the wall regarding needing an ORCID to do so. A few journals are starting to require ORCIDs for authors as well.
You could also consider a profile at an alternative-metrics aggregator such as ImpactStory.
(Disclaimer: I have an ORCID and an ImpactStory subscription, and consider one of the ImpactStory founders a friend. Nobody pays me to recommend either, however.)