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Well, you're in luck, because Buzzfeed senior designer, F.A.T. denizen, and Ex-Blocker developer Greg Leuch has whipped up a fun little hack that will let you do just that.
All one has to do is create a GIF using 3fram.es, resize the GIF on the F.A.T. website, and download it for easy uploading to Twitter.
According to Leuch, the project has been used to process nearly 400 avatars already. "Hoping to spend some time tonight and make the resizing utility do some more advanced features and *fingers crossed* sync it to their Twitter account and auto-upload their new animated avatar as their profile photo," Leuch tells us via e-mail.