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.

日本人でAndroid使ってる人あんまりいないだろうけど、GIF画像貼れなくて困ってる人いたら参考にしてください