Using our API's you can get the contacts who sign up on your web contact form on your site into our system. The way to do this would be to use the Contact Collection URI.
You would need to do a POST HTTPS call to this URI, more information what to post can be found here. Please keep in mind that this usually does require the ability to use some kind of web scripting language such as PHP or ASP.net.
You could do this post after they are added to your database, and it would allow you to have them added to your end and ours at the same time.
If you have any further questions regarding this please let me know and I can try to help further.