The simple answer to the question in the title is no. No, there is no way to see who visits your Facebook profile. Facebook simply does not allow tracking applications on their website, and will reject any application submitted to them for approval if it contains code with the capability of doing so. In the unlikely event that any trackers do by miracle get passed the facebook application moderators, you can bet your life that it wouldn't take them long at all to find it and remove it.
Facebook Trackers Disallowed
“Is there any way to see who has been viewing my profile? Can people see that I looked at theirs?There are, as suggested, some applications with very limited functionality. These will analyse and present statistics on those who are most active on your profile, e.g. those who 'like' your posts the most and comment on your wall the most. These provide you with no information whatsover which you cannot ascertain yourself by simply reviewing your past notifications.
Facebook does not allow users to track profile views or see statistics on how often a particular piece of content has been viewed and by whom. Third party developers, however, may offer applications that provide some of this functionality. Please keep a few things in mind when using these, however:
1. Applications cannot track profile views for users who simply visit another person's profile. Facebook has made this technically impossible.
2. In order to be tracked by an application, you must explicitly agree to allow the application to access your information.
3. Adding an application that provides this functionality is purely optional. If you do not want to participate, please do not add the application to your account.”