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.

Add this code to your child theme’s functions.php file or via a plugin that allows custom functions to be added, such as the Dessky Snippets plugin. Please don’t add custom code directly to your parent theme’s functions.php file as this will be overwritten completely when you update the theme.

/**
 * Add custom sorting options (asc/desc)
 */
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'] ) ? wc_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;
}