Get custom taxonomy link in wordpres

Try below code, i hope it would helpful for you.

 <?php $args = array('taxonomy' => 'news'); ?>
<?php $tax_menu_items = get_categories( $args );
foreach ( $tax_menu_items as $tax_menu_item ):?>
<li>
 <a href="<?php echo get_term_link($tax_menu_item,$tax_menu_item->taxonomy); ?>">
  <?php echo $tax_menu_item->name; ?>
 </a>
</li>
<?php endforeach; ?>
</ul>