The maximum file size for avatars is 50KB, yours is over 300KB, so the avatar would not fit with the rules as posted here:
Well there is no way, since then it will not be the same, that avatar has a big file size because it like it is. Though having it as a signature sure does fit. I am sorry, you have to pick another avatar that does not go over the limit.
...or you could find a gif size editor online so that it reduces the overall size of your gif. I tried it a while back because I had the same problem with a buggy gif, the only issue with reducing the gif size is the quality of the gif itself. It gets poorer and poorer in quality xD. If you find a decent gif size editor online and it works succesfully without effecting the quality much please let me know too, EMS! :3