I'd like show tag symbols rather than tag symbols. For example, Rather than the tag text "Illustrator" I must show Illustrator icon. Any help could be cordially appreciated.

You most likely will have to make a symbol for every tag, then make use of the tag title to construct a road to the icon.

<img src="/icons/<?php echo $tagName; ?>.png" />

you could do this by using tag images wordpress plugin