According to Fast Company, it is not possible for Facebook users to see if other users have searched for them. Apps or programs that claim to show who is searching for who are not accurate. Although Facebook does keep data on user searches, this information stays private, and Facebook users are only able to see who they have searched for themselves.
Many of the means through which Facebook presents data about other users, such as the friends who appear most often under the "Friends" section on a user's profile or show up when a search is made, are commonly thought to reflect the frequency of profile views. However, the frequency with which other users are displayed under the "Friends" heading on a profile page is actually dictated by many other specific parameters, including amount of wall posts, comments and similarly attended events. Search results, including which users pop up after only a couple of letters have been typed in the search box, are in fact dictated by profile views. However, viewing someone else's profile frequently only affects the user's own search results, not the results of the person whose profile they are viewing. Facebook does record data about every action users take while on the site, but this data is inaccessible to other users.