At this point in time, you can only do that via FB or gravatar.com.
If you sign in with FB or are using gravatar.com, you can go to EDIT PRIFILE by clicking the 3 short bar icon displayed on the upper left corner of GA.ME screen.
You’ll have to go and sign up here http://en.gravatar.com/. From there, you can upload a picture from your computer or the internet, and select it to be your avatar. Once you’ve done that, whichever picture you selected should be your profile picture here.