taxonomy-product_cat.php file not working

Is your taxonomy-product_cat.php file not working? All you may need is to add your WooCommerce theme support to your theme function’s file.

Add theme support for WooCommerce taxonomy templates

To allow your taxonomy-product_cat.php file to register, you must add the WooCommerce theme support to your WordPress theme’s functions.php file.

add_theme_support( 'woocommerce' );

Refresh your permalinks

You could try to refresh your permalinks after you’ve created the file in your WordPress theme’s root directory.

You can do this by visiting your WordPress Dashboard>Settings>Permalinks and clicking Save Changes without changing anything.