Modify functions.php to add a term ‘uses-theme’ set to theme name on post save

I would create custom post meta for this data, as it seems the most logical. It should be easy to implement, since you don’t need to expose this custom meta data to the UI; just add a callback to save_post.

You can use wp_get_theme() to retrieve information about the current Theme. This function returns an instance of the WP_Theme object.

function wpse76752_add_post_meta() {
    global $post;
    $current_theme = wp_get_theme();
    update_post_meta( $post->ID, '_current_theme', $current_theme->Name );
}
add_action( 'save_post', 'wpse76752_add_post_meta' );

Note that I prefaced the custom post meta key with an underscore. This prevents the meta key from being listed in the “custom fields” dropdown in the Edit Post screen. (Basically, it makes it an “internal” post meta key, that is hidden from the UI unless you explicitly expose it.)