The dramatic Oscar-winning tune beat Ennio Morricone's The Good, The Bad and the Ugly and Leonard Bernstein's composition for West Side Story, which were ranked second and third, respectively.
The top five was rounded out by the main Lawrence of Arabia theme by Maurice Jarre and Bernard Herrmann's Vertigo.
A Bbc spokesperson says, "With almost a quarter of the audience votes, John Williams' Star Wars Theme topped a list that spans 64 years of cinema soundtrack history. Williams' soundtrack remains to this day the highest-grossing orchestral film music recording of all time and secured him his third Academy Award in 1977."
Music from The Dark Knight Rises, Psycho, Grease and The Sound of Music also appear in the Sound of Cinema poll, which was voted for by the public.