Provides a function to add a 'publish' link to posts for use on the front end

frontend-publish.php

<?php
/*
 * Provides a function to add a 'publish' link to posts. 
 * Use sh_frontend_publish() to display the link
 *
*/

function sh_frontend_publish(){
     $post_id = get_the_ID();
     if( 'draft' == get_post_status($post_id) && current_user_can('edit_post',$post_id) && current_user_can('publish_posts') ){
          $url = add_query_arg(array(
                  'action'=>'sh_frontend_publish',
                  'post'=>$post_id
               ),
               home_url());
          $url = wp_nonce_url($url, 'sh_frontend_publish_'.$post_id);

      echo  "<a href='{$url}'>Publish</a>";
     }
}
    


    //Run the publish function only if the action variable is correct.
    if(isset($_GET['action']) && $_GET['action']=='sh_frontend_publish'){
       add_action('init','sh_frontend');
    }

    function sh_frontend_publish_draft(){
         //Get the post's ID.
         $post_id = (isset($_REQUEST['post']) ?  (int) $_REQUEST['post'] : 0);

        //No post? Oh well..
        if(empty($post_id))
            return;

        check_admin_referer('sh_frontend_publish_'.$post_id, '_wpnonce');

        //Check user permissions
        if (!current_user_can('publish_posts') || !current_user_can('edit_post', $post_id) )
            wp_die("You can't do that"); 

        //Publish post
        $post = get_post($post_id,ARRAY_A);
        $post['post_status'] ='publish';
        wp_update_post($post)

        //Redirect to published post
        $redirect = get_permalink($post_id);
        wp_redirect($redirect);
        exit;
    }
?>