Display a specific product tag on shop/category archive page.

functions.php

<?php

// Display a specific product tag on shop/category archive page.
add_action( 'woocommerce_before_shop_loop_item', 'woocommerce_poruct_tags_before_shop_loop', 7 );
function woocommerce_poruct_tags_before_shop_loop(){

	// get product_tags of the current product
	$current_tags = get_the_terms( get_the_ID(), 'product_tag' );
	//only start if we have some tags
	if ( $current_tags && ! is_wp_error( $current_tags ) ) { 

	    //create a list to hold our tags
	    echo '<div class="product_tags">';
	    //for each tag we create a list item
	    foreach ($current_tags as $tag) {
	        $tag_title = $tag->name; // tag name
	        $tag_link = get_term_link( $tag );// tag archive link
	        echo '<a href="'.$tag_link.'">'.$tag_title.'</a>';
	    }
	    echo '</div>';
	}
}