All Tennis Players How Many Grand Slams Has Roscoe Tanner Won? Leonard Roscoe Tanner (born October 15, 1951) is a retired American tennis player.Roscoe Tanner has won 1 Grand Slam. Facebook Twitter Email How Many Grand Slams Has Aryna Sabalenka Won? How Many Grand Slams Has Carlos Alcaraz Won? How Many Grand Slams Has Elena Rybakina Won?