Facebook privacy question?

[You Betcha!]

You can't. It's either everyone can search for you or no one.

You can try a few other things though to see if the unwanted requests stop. Change all your privacy settings to friends only..There could be something on your profile that makes them want to add you. Go to Account>Privacy Settings>Customize Settings. Change all the settings to friends only, including the photo album settings (found in the middle of the page). Also go to Account>Privacy Settings>at the top of the page it says connecting on facebook with a view settings option. Click that and change most of (or all) the settings to friends only. You could try changing the "send you friend requests" setting to friends of friends. That will take away that button from the spammers/pervs. You could then leave the "who can send you messages" to everyone in case a friend that you dont have any mutual friends with wants to add you.