What you need for this is first of all the SimpleTags plugin and an icon (quick image search). You will need to edit the file simpletags.php in your ‘wp-content/plugins’ folder.

Look for this:
$pre_replacement = '<p>';

and replace it with this:
$pre_replacement = '<p><img src="path/to/technorati.gif" width="in pixels" height="in pixels" alt="Technorati"> ';

The result will look like this:

Technorati tags with icon

and like at the bottom of this post.