How to subscribe to blog on external website

Hello

I’m trying to figure out whether it is possible to add a subscribe to blog button on an external website.

My current website has a contact page http://compsys.co.uk/contact.php

My blog is at http://www.compsys.co.uk/blog and using Jetpack.

What I’m trying to is put a tickbox into http://compsys.co.uk/contact.php with an option “Click here to subscribe to my blog”

To show what I’m trying to achieve this is a link from one of the Hubspot pages http://offers.hubspot.com/call-to-action-templates?__hstc=20629287.c049a3db4b0ef1c0349aa22501e71f41.1383900628176.1383900628176.1383907214805.2&__hssc=20629287.4.1383907214805&__hsfp=2956331461
The contact form on the right hand side is what I am trying to do.

Is this possible with WP/Jetpack/Twentytwelve please ?

Regards
Graham