Specifically academic alternative to LinkedIn

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.)