Delete user from frontend

Taken directly form the wp_delete_user documentation:

if(is_user_logged_in() && !empty($_GET['DeleteMyAccount'])) {
    add_action('init', 'remove_logged_in_user');
}

function remove_logged_in_user() {
    require_once(ABSPATH.'wp-admin/includes/user.php' );
    $current_user = wp_get_current_user();
    wp_delete_user( $current_user->ID );
}

Things to note:

• Your code didn’t check if the user was logged in or not
• by the time you’re printing the remove user link, the init action has already happened and finished, so your delete user wouldn’t work. That part of the code needs to be ran earlier, say in functions.php or a plugin

edit:

If you can place this in your themes function file:

add_action('init', 'remove_logged_in_user');

function remove_logged_in_user() {
    require_once(ABSPATH.'wp-admin/includes/user.php' );
    $current_user = wp_get_current_user();
    $success = wp_delete_user( $current_user->ID );
    wp_die('wp delete gave: <pre>"'.print_r($success).'"</pre>');
}