add-custom-sorting-options.php

/**
 * Add custom sorting options (asc/desc).
 */
function wb_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 ( $orderby_value === 'random_list' ) {
		$args['orderby']  = 'rand';
		$args['order']    = '';
		$args['meta_key'] = '';
	}
	return $args;
}
add_filter( 'woocommerce_default_catalog_orderby_options', 'wb_custom_woocommerce_catalog_orderby' );
add_filter( 'woocommerce_catalog_orderby', 'wb_custom_woocommerce_catalog_orderby' );

/**
 * Sorting by custom options.
 */
function wb_custom_woocommerce_catalog_orderby( $sortby ) {
	$sortby['random_list'] = 'Random';
	return $sortby;
}
add_filter( 'woocommerce_get_catalog_ordering_args', 'wb_custom_woocommerce_get_catalog_ordering_args' );