Actually Facebook not allow to put or post GIF file on facebook,but now you can post image with GIF format to Facebook by using code.My friend on balikta.net give this tutorial,thanks for master balikita.net.
This trick is really simple,Follow these instruction:

1.Visit this link: Click here

2.Find google custom search box on

3.Type "Bank" on google custom search

4.Click "Bank link",activate GIF image on the "Bank link",wait about 15 minute....!

5.GOOD LUCK...!

news update:
Download facebook script,click here