It is your house. Children, as long as they live in your house, are accountable to you. You have every right to do anything you want to in their room. If they would like to rent the room from you (I would divide the square footage of their room by the square footage of the house. That percentage of your house payment/rent could be a gauge for his rent, but that is just my opinion--you may have a better plan), then that might be different. I understand that a 21-year-old might have some privacy issues because of growing independence. Is he in college? Does he have a job? Is he making enough to be out on his own?
These are all questions you might consider. Your son is not going to get any less independent as time goes by. When he is at the point where he cannot submit to house rules, perhaps it is time to launch.
