Tags are generally already supported and included in single CPT’s so you don’t need to add anything however you can use this code if you like.
Add this line to your code:
'taxonomies' => array('post_tag')
So your code will look something like this:
add_action( 'init', 'wpsites_custom_post_type' );
function wpsites_custom_post_type() {
register_post_type( 'your-cpt',
array(
'labels' => array(
'name' => __( 'Your CPT', 'wpsites' ),
'singular_name' => __( 'Your CPT', 'wpsites' ),
),
'has_archive' => true,
'hierarchical' => true,
'menu_icon' => 'dashicons-heart',
'public' => true,
'rewrite' => array( 'slug' => 'your-cpt', 'with_front' => false ),
'supports' => array( 'title', 'editor', 'author', 'thumbnail', 'excerpt', 'trackbacks', 'custom-fields', 'revisions', 'page-attributes' ),
'taxonomies' => array( 'your-cpt-type', 'post_tag' ),
));
}
Replace all instances of your-cpt with the name of your custom post type.