Google+ has supported animated gifs since the very beginning and along with its major app update, has also announced the ability to have animated profile photos. When you upload an animated GIF as your profile photo, it will animate on your profile page on both mobile and desktop. Fortunately, Google+ made it to where your photo will not animate within the stream, otherwise that could be incredibly distracting. If you aren’t sure how to go about making an animated GIF, simply doing a Google search for “How to create a gif” will point you in the right direction.
Source: Google+ Page