You can't cast GIFs from the Android app.
However, you can display it by inserting the URL of the GIF image.
By the way, Farcaster itself stores GIFs on Cloudflare, but if you register and post them yourself, you will have to pay for it.
So I recommend gyazo.
https://gyazo.com/
Image files are also permanently stored and can be used for free.
I made a video to make it easier to understand, so please take a look.
As you can see in the video, all you have to do is add ".gif" to the end of the URL of the GIF image you posted to gyazo and cast it.

I'm Japanese Graphic designer. I use translations to cast, so sorry if I use strange English. /likewen

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