How to include a file only on dashboard widgets page?

You can use the following code. Asuming that the css file style.css is inside the css folder of your theme:

function wpse_126614_enque( $hook ) {
    if ( 'widgets.php' != $hook ) {
        return;
    }
    $template_url = get_template_directory_uri();
    wp_enqueue_style( 'admin-style-widget', $template_url . '/css/style.css' );
}
add_action( 'admin_enqueue_scripts', 'wpse_126614_enque' );