If you made the GIF just nope and it is in your desktop. You need to upload it to some websites like imgur or photobucket because you cannot upload GIFS for a signature (you can for a avatar though). Then use the following code to put that GIF as a signature like Lyke said.
PHP:
[IMG]Link to the picture[/IMG]
Also, remember that the GIF/picture should not exceed 600 x 300.