I don't think you can set a gif as your forum avatar. I haven't really seen anyone else doing it so I assume it's not possible. ;;
edit: omg i just realized
From what was said below, there have been people using tiny gif icons of their characters. But like Lotor said, you might need to get a small gif of it. Also make sure that you're using [img] and [-/img] (without the "-" that's there) instead of [gif] and [/gif]