Facebook answers this question and includes a separate question that it words slightly differently, “Can I know who’s looking at my Timeline or how often it’s being viewed?”
“Your Timeline is your collection of the photos, stories, and experiences that tell your story.”
The links to the questions above and the following list of questions are on a Facebook.com page titled “Common Myths About Facebook.”
“Will Facebook ever charge for service?
Do advertisers have access to my personal information?
Does Facebook sell my information?
Can people tell that I’ve looked at their Timeline?
Can I know who’s looking at my Timeline or how often it’s being viewed?”
Can people see my private messages on my Timeline?
What personal information is shared with sites that use social plugins?
The app I’m using says I need to download something, fill out a survey or sign into Facebook again to see special content. Is this true?”
“No, Facebook doesn’t let people track who views their Timeline. Third-party apps also can’t provide this functionality. If you come across an app that claims to offer this ability, please report the app.”