Upload your banner into Media Library. (Media>Add new) When image is uploaded click on Edit link and you will find direct link to your image on the top right.
Then add this code into your text widget.
<a href="http://website-you-promote.com" target="_blank" rel="nofollow"><img src="http://your-image-direct-link.jpg" alt="Your Alt Name"></a>
Make sure to change link and image location, as well as alt name.