Now you can make your own GIFs on Facebook. You can make Facebook GIFs by just using the camera in Facebook App.
The Facebook GIFs feature is presently available to a small group of people for testing but it will soon roll out to other users as well. In order to make GIFs on Facebook you will swipe left on your phone app to open in-built camera app.
At the top of the camera you will see two options: Normal and GIF. Just tap on GIF to make your own creations and adorn them with filters from Facebook
Little late but Facebook has jumped into the creation of GIFs and will roll out this feature publicly in coming weeks.