click tags for custom post types

You have to register the post_tag taxonomy for your post type:

<?php
register_taxonomy_for_object_type( 'post_tag', 'portfolio'  );

Now you’ve got post_tag taxonomy shared with regular posts and other post types for which tags where registered.

If you want to use custom taxonomy for example, portfolio-tag, which belongs to the portfolio custom post type only:

<?php
function portfolio_tags()
{

    $labels = array(
        'name' => 'Portfolio Tag',
        // More labels goes here
    );

    $args = array(
        'labels' => $labels,
        // More arguments goes here
    );

    // agrs: taxonomy key, custom post type, arguments
    register_taxonomy( 'portfolio-tags', 'portfolio', $args );

}

add_action( 'init', 'portfolio_tags', 0 );

For register_taxonomy() arguments see the Code Reference.