Non Users Delete Posts

How can I allow non users to delete posts?

I am currently using this code:

<?php
  global $wp_query;
  $cat = get_the_category();

  if ($cat[0]->cat_ID == 86){
      $url = get_bloginfo('url');
      echo "<a>ID) . "'>Delete post</a>";
 }
?>

This adds a delete link if the current post is in a certain category. It works perfectly but It requires a user with edit privileges to be logged in. How can I change this to allow for regular, non registered users to delete posts?

Any help is appreciated.