Sure and you can hang a sign in your front lawn that's says you're an a**h*** if you want, but most people thankfully aren't and don't.
Seriously - yes it's your right but as a sportsman, if that's your only reason, it's lame.
If my name isn't on the deed, I give zero f***s about what goes on there. If my name isn't on the deed, I have zero standing in calling someone an a**h*** because he posts his property.
Property rights trump hunting eight days a week and that owner doesn't need a reason.
Don't like it? Buy it.
*no, my property isn't posted, although it does have some old and incorrect no trespassing signs by the previous owners.