In many card shops, you’ll occasionally come across a card that looks like it’s moving when you tilt it from side-to-side.
The same principal (lenticular printing) is used by Gifpop! who use this old method to bring modern gifs to life.
They can print 10 frames in total so you can’t have anything too long — just a few seconds is ideal. Your chosen gif can be printed on five sizes of card ranging from a business card to a 5″ square. They ship internationally but it’s a lot cheaper if you live in the United States.