What you are asking for doesn't make sense.
How do you think free use of this site works? Your phone connects via your carrier's network, so they know which site you are requesting connection to and can exclude that traffic from their billing. Now if you used a VPN app like psiphone all that would mean is that they'd not know which website you were connecting to, just that you were sending traffic to/from whatever server psiphone were using. They'd still know how much data you were transferring, and they'd still know that it wasn't from the free website, so they'd still bill you for it. Nothing you do on your phone can change that. In fact the only difference it would make is that if you actually visited the free website via a VPN they'd not know that you were looking at the free site and so they'd bill you for that as well.