you would have to install a third party app on his phone
it may or may not be legal
now on my parenting 101
ask your sone to view the texts
compare them to the timestamps on myverizon
if any are missing tell him not to delete them again until you review them
if he does take away the phone
I see no reason to think this would not be legal.
Your son is not old enough to enter into a cell phone agreement with Verizon, so I assume YOU are the account owner. There is no law keeping you from putting an app on YOUR phone to track the texting history from YOUR phone. Whether or not he will be able to notice this app running in the background and disabling it is another matter entirely.
If you are unable to find/use an app for such a task, then what mdram4x4's suggestion is the only way. Of course, if your son only has a basic phone, the chance for an app which would do this is not very likely.