The track, recorded by the former 'Beatles' member and his band 'Wings', received more than a quarter of all the votes.
The 1973 film starred Sir Roger Moore opposite Bond girl Jane Seymour, the BBC reported.
Carly Simon's 'Nobody Does It Better' from 'The Spy Who Loved Me' was runner-up, while Dame Shirley Bassey's 'Goldfinger' came in third.
The poll is one of a number of events to mark Bond's 50th anniversary.
McCartney also sand 'Live and Let Die' at the end of the Queen's Diamond Jubilee Concert outside Buckingham Palace earlier this year.