I'll start by assuming you already know how to create and upload workshop content for Terraria.
If you don't, this is not the guide for you.

First, you need a gif. There are plenty of ways to create them; I either create them by hand or record them from ingame with a program called ScreenToGif.

This is the gif we'll be using.


We start on our upload page and click on "image: Empty".


Then we browse to the location our gif is saved.


But wait, our gif is nowhere to be found!
Don't worry, there is a simple solution.

See this little box here?


Change it to this.


And voila! There's our gif.


If you can't change the box, you can also just type the full name of your file in the filename field.


Then click "Open."

There's your gif, sitting pretty in the icon field.