These are the songs that reached number one on the Top 100 Best Sellers chart in 1962 as published by Cash Box magazine.
Issue date Song ArtistJanuary 6 The Twist Chubby CheckerJanuary 13 January 20 January 27 February 3 Duke of Earl Gene ChandlerFebruary 10 February 17 February 24 March 3 March 10 Hey! Baby Bruce ChannelMarch 17 March 24 March 31 April 7 Slow Twistin' Chubby Checker with Dee Dee Sharp April 14 Good Luck Charm Elvis PresleyApril 21 Johnny Angel Shelley FabaresApril 28 Mashed Potato Time Dee Dee SharpMay 5 Soldier Boy The ShirellesMay 12 May 19 Stranger on the Shore Mr. Acker Bilk May 26 I Can't Stop Loving You Ray CharlesJune 2 June 9 June 16 June 23 June 30 The Stripper David Rose & OrchestraJuly 7 July 14 Roses Are Red (My Love) Bobby VintonJuly 21 July 28 August 4 August 11 Breaking Up Is Hard to Do Neil SedakaAugust 18 The Loco-Motion Little EvaAugust 25 September 1 September 8 Sherry The Four SeasonsSeptember 15 September 22 September 29 October 6 October 13 October 20 October 27 Monster Mash Bobby (Boris) Pickett & Crypt-KickersNovember 3 November 10 November 17 Big Girls Don't Cry The Four SeasonsNovember 24 December 1 December 8 December 15 Return to Sender Elvis PresleyDecember 22 Limbo Rock Chubby CheckerDecember 29 Telstar The Tornadoes
See also 1962 in music List of Hot 100 number-one singles of 1962 (U.S.)
References http://www.cashboxmagazine.com/archives/60s_files/1962.html