Adding CSS Class name to Post Tags

add_filter( 'term_links-post_tag', 'paulc_add_custom_class' );
function paulc_add_custom_class( $links ) {
	$new_links = array();
	foreach ( $links as $link ) {
		preg_match( "|<a.*[^>]*>([^<]*)|i", $link, $matches );
		$class = strtolower( $matches[1] );
		$link = str_replace( 'rel="tag"', 'class="' . str_replace( " ", "-", $class ) . '" rel="tag"', $link );
		$new_links[] = $link;
	}
	
	return $new_links;
}

Simply add the above code into the functions.php file of your active theme. It will add the tag slug to class parameter of anchor tag.