Using Icons and Links on my Linklist

Is there an easy way to use icons without text or URL (except in hypertext) to link to sites relevant to my own? I’m using the links sidebar widget, and I can add the image to a link, but then there’s an image AND text, which looks pretty cluttered. When I take out the text “name” for the link, wordpress inserts the url for the link as text.

I want the user to just click the icon to follow the link. (most of the icons say the name of the website, so I don’t need the text).