It sounds like you want a signature link.
There's no specified dimensions for such a thing (though I believe the height has to be below a certain amount or else the signature will scroll).
Basically you make your image, get your URL, and arrange them as such:
[url=LINK ADDRESS HERE][img]IMAGE LINK HERE[/img][/url]
You'll need to use an image hosting site for the image, such as imgur or tinypic.