Add crossorigin to SCRIPT tag

script_loader_tag or script_loader_src filters are there to let you tweak the HTML of the script easily so you can add custom attributes:

add_filter('script_loader_tag', function($tag, $handle){
    switch ( $handle ) {
        case 'foo':
            $tag = preg_replace(
                '/src=[\'|"|]/i',
                'crossorigin $0',
                $tag
            );
            break;
    }

    return $tag;
}, 10, 2);

To avoid conflicting with other plugins, pass unique handles to the script/style register/enqueue function, foo in your case:

wp_register_script('foo', 'http://cdn.domain.com/script.min.js', null, '1.2.3');