It is now once again possible to upload an avatar to the forum. You must be a full member or above to upload an avatar. Go to this page (also linked in your "Forum Profile Information" settings):
https://bitcointalk.org/index.php?action=avatar

You can only upload new avatars: you can't choose one from the server or use a link as you could before. (If you are currently using one of these types of avatars, the upload avatar page will say that you don't have an avatar.) Also, uploaded avatars are not resized: they are simply rejected if they are too large.