To add links to your Tumblr bio, you'll need to use a simple HTML code. Tumblr doesn't give you any sort of built-in way to add links yourself, so you'll have to copy and paste the code in manually.

you can add a link to any image file, including JPGs, PNGs and GIFs. If you're creating a clickable image on your business website, a fast way to do it is to type the code yourself in HTML.