Make a link table in MySQL, link between Users and Movies.
USER
ID, username, password, fname, lname
MOVIE
ID, name
LINK_MOVIE_N_USER
ID, movie_ID, user_ID
Store the user_ID in the COOKIE, everytime they try to rate a movie, check to see if that link ( user_ID = $_COOKIE['ID'] and movie_ID = $my_movie_ID ) already exsists.