Is there a feature like this available? My community actively markets over Instagram, and I would like to have followers be able to sign in through their IG accounts.

One does not currently exist (at least, it's not built in or available for sale via the Marketplace), but it is certainly possible to create one if you are a developer. There is pretty extensive documentation here. If you are not a developer you could probably contract it out for $100-$200 or so (just guessing based on complexity and going rates).