add_filter( 'woocommerce_get_catalog_ordering_args', 'custom_woocommerce_get_catalog_ordering_args' );
function custom_woocommerce_get_catalog_ordering_args( $args ) {
  $orderby_value = isset( $_GET['orderby'] ) ? woocommerce_clean( $_GET['orderby'] ) : apply_filters( 'woocommerce_default_catalog_orderby', get_option( 'woocommerce_default_catalog_orderby' ) );
  if ( 'random_list' == $orderby_value ) {
    $args['orderby'] = 'rand';
    $args['order'] = '';
    $args['meta_key'] = '';
  }
  return $args;
}
add_filter( 'woocommerce_default_catalog_orderby_options', 'custom_woocommerce_catalog_orderby' );
add_filter( 'woocommerce_catalog_orderby', 'custom_woocommerce_catalog_orderby' );
function custom_woocommerce_catalog_orderby( $sortby ) {
  $sortby['random_list'] = 'Random';
  return $sortby;
}



This example code shows how you can add an order option for ‘random’, but this also works in similar ways for other ways to order your products on the catalog page. To learn more about the default ‘orderby’ options please see the WordPress Codex Class Reference.