McCartney recorded the track with his band Wings for the 1973 Bond film of the same name, starring Roger Moore as 007.
The track pulled in more than a quarter of the votes in the BBC Radio 5 Live poll.
Carly Simon's 'Nobody Does It Better' from 1977 film 'The Spy Who Loved Me' came second while Shirley Bassey's 'Goldfinger' for 1964 film of the same name came third.
'A View to a Kill' by Duran Duran in 1985 was forth while
Alicia Keys and Jack White's 'Another Way to Die' from 2008 film 'Quantum of Solace' claimed the fifth spot.
'The World Is Not Enough' by Garbage in 1999 and 'Diamonds Are Forever' again by Shirley Bassey in 1971 came sixth and seventh in the poll.
'You Only Live Twice' by Nancy Sinatra in 1967, 'For Your Eyes Only' by Sheena Easton in 1981 and 'You Know My Name' by Chris Cornell for 2006 film Casino Royale rounded off the top-ten list.
The poll marks 50 years of Bond movies since 007 first appeared on cinema screens with 'Dr No'.
The 23rd Bond film 'Skyfall', which marks Daniel Craig's return as the dashing spy for the third time, is set to release on November 2.
Singer Adele is reportedly recording the theme song for 'Skyfall'.
