If your theme uses body_class
and post_class
then you should have CSS enough to do this.
Make a <div>
for your icon.
<div class="mycategoryicon"></div>
Add some style.
.category-slug .mycategoryicon {
height:32px;
width:32px;
background:#ffffff url('slug-icon.jpg') no-repeat;
}
The “slug” part of the class name should be your actual category slug. Height and width can of course be whatever you need.