why complicate your life? Assuming you're using the latest WP version, simply do this:
1- create the category if you don't already have it
2- edit your links by going to yourdomain/wp-admin/link-manager.php. When you hover over your links (which will be assigned to Blogroll by default) you'll see the words
edit|delete shows up. Click on edit.
3- assign to each link the category where you want the link to show up. You'll see other options as well, like Target, Link Relationship, Images (ie for banners), ranking and such
That's it. No plugin, no code needed
