It's been broken since last week's update. At first avatars started to glitch (like mine). It wasn't long after that when the ability to set new avatars disappeared. I'd assume Jagex would be on the case by now, but as to which team has to look into it (web or game) I have no idea.
Mod Lyonsaid: So good news - the relevant team tried a very simple fix and it seems to have worked.
Updated pictures will have odd textures for some time, it is not a priority for us with mobile being the main focus. If there's any updates I'll try to remember to post in here for those who want to "fix" theirs
So, its "fixed" as in a picture taken ingame will now cause the picture on the forums to update, though the fix so they look correct may be a bit.