// We get a list taxonomies on the search box
function get_tax_by_search($search_text){

$args = array(
    'taxonomy'      => array( 'my_tax' ), // taxonomy name
    'orderby'       => 'id', 
    'order'         => 'ASC',
    'hide_empty'    => true,
    'fields'        => 'all',
    'name__like'    => $search_text
); 

$terms = get_terms( $args );

 $count = count($terms);
 if($count > 0){
     echo "<ul>";
     foreach ($terms as $term) {
       echo "<li><a rel="nofollow" href='".get_term_link( $term )."'>".$term->name."</a></li>";

     }
     echo "</ul>";
 }

}

// sample
get_tax_by_search('Foo');