Facebook just announced that you'll be able to use GIFs as your profile photo. According to Wired Magazine:

The most significant update for profiles is easily that your photo no longer has to be a photo at all—now, you can have a profile video. “You’ll be able to film a short, looping video clip that will play for anyone who visits your profile,” Facebook writes in a blog post announcing the changes. This is not a drill—I repeat, this is not a drill: You can soon have a GIF profile photo on Facebook. It also might be the single most-used home for iPhone Live Photos.

Sources: Wired