There isn't a way to do this directly on iOS. What you can do that is the closest thing to what you want to achieve is to follow these steps:
- Go to Settings > General > Restrictions > Enable Restrictions and create a passcode that only you will know (and it should be different from the passcode that has been set on your son's iPhone, if there is one).
- Then deselect the following items: Safari, iTunes Store, iBookstore, Installing Apps, Deleting Apps, in-App Purchases, Siri, and FaceTime (of course, deselect whatever you see fit, but my example is an extreme example).
- On the same Restrictions menu, go to Accounts and tap "Don't Allow Changes".
- Go to Restrictions once again, and go to Cellular Data Use and tap "Don't Allow Changes".
- Finally, go back to Restrictions, scroll down to the bottom of the page, and tap the following switches under Game Center: "Multiplayer Games" and "Adding Friends."
I'm assuming that you don't want your son to use any form of Internet on the iPhone AT ALL. This will limit the iPhone to the most limited form as possible. I can't guarantee that your son will not be able to use the Internet in some way, shape, or form, but at least you have now severely limited the chances.