Register wordpress users on page that is not inside wordpress directory

Ok.. I know it sounds bizarre, but is there a way to create a registration form on a page that is in the same server / public_html directory but part of a different php script?

I have a shopping cart installed that is fully cusotmized. I would like to create a “register for our blog” form within the checkout process. I do not need someone to hold my hand through it, but I have found NOTHING in the way of registering users.

Any help is greatly appreciated.