Until recently there was no way of embedding animated GIFs on Facebook pages. Thankfully, Giphy is a site that uses a workaround to help you put GIF animations directly on a Facebook wall, group, or message.
Search for a GIF to Publish
Giphy uses a database filled with GIFs from around the web. It sources images from Tumblr, Reddit, and various user submissions. Just search for what you’re looking for, or browse through the categories.
Once you’ve found the image you like, hit the share to Facebook button.
Posting to Facebook
A new window will open where you can place the GIF on your own timeline, a friend’s timeline, to a group, or as a private message. You can also write a description for the GIF.
Get it animating
Hit the Share Link button and the GIF will be posted to Facebook. It will show up as a preview.
Hit the play button and Giphy will turn the image into a looping Flash animation, similar to Youtube. Yes, it's just a wrapper, but it fully simulates a real animated GIF.
What animations are you thinking about posting to Facebook?