Facebook offers a variety of granular privacy settings so that you can control which friends -- and strangers -- can and cannot interact with you or see content that you post. As of March 2011, Facebook lets you choose between allowing anyone to initiate a friend request or restricting friend requests to just friends of friends. By default, anyone can add you as a friend. If someone who is not your friend tells you that they do not see an "Add as Friend" button when she visits your profile, and you want it visible, you may need to toggle this setting.
Log in to your Facebook account.
Click the "Account" button at the top of the screen.
Click on "Privacy Settings."
Click "View Settings" under "Connecting on Facebook."
Choose "Everyone" from the drop-down list next to "Send you friend requests." Anyone is now able to add you as a friend, though you must confirm that request to create the friendship.
- Screenshots By Crosswised