I was wondering if it’s possible to implement card.js on WordPress

by

Seems like you have misplaced the card jquery library. You can include the js using wp_enqueue_script in WordPress. 

wp_enqueue_script( 'jquery-card-script', get_stylesheet_directory_uri() . '/js/card.js', array( 'jquery' ), '1.0.0', true );

Use the above code in your child theme functions.php and
call your card from your main js file.

new Card({
        form: document.querySelector('form'),
        container: '.card-wrapper'
    });