mero-S

function get_tags_in_cat($cat_id)
{
    $posts = get_posts( array('category' => $cat_id, 'numberposts' => -1) );
    $tags = array();
  
    foreach($posts as $post)
    {
        $post_tags = get_the_tags($post->ID);
        if( !empty($post_tags) )
            foreach($post_tags as $tag)
                $tags[$tag->term_id] = $tag->name;
      
    }
    asort($tags);
    return $tags;
}

<?php
    $cat_id = get_query_var('cat'); // получаем ID текущей категории   
    $tags = get_tags_in_cat($cat_id);
    foreach($tags as $tag_id => $tag_name)
        $tags_print[] = '<a href="' .get_tag_link($tag_id). '">' .$tag_name. '</a>';
    echo implode(', ', $tags_print);
?>