Cam Newton has scored the most career rushing touchdowns by a quarterback, with 73 touchdowns.

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which quarterback had the most rushing touchdowns alltime
NewtonYoungKempMcNairRoteVickCunninghamGroganRodgersCulpepperElwayGrahamTittleStewartBradshawTarkentonGabrielMcNabbAllenBradyGarciaPrescottBrees7343403737363535343433333332323230292826262525
NAMEGPRUSH TDRUSH YDSATTYPCRUSH YDS/GREC YDSRECTRGAVGREC YDS/GREC TD
Cam NewtonCam Newton143735,4631,0875.038.2683322.70.51
Steve YoungSteve Young169434,2397225.925.12201.00.00
Jack KempJack Kemp122401,1503563.29.4-91-9.0-0.10
Steve McNairSteve McNair161373,5906695.422.34114.00.00
Tobin RoteTobin Rote149373,1286354.921.028214.00.21
Michael VickMichael Vick143366,1098737.042.71220.50.00
Randall CunninghamRandall Cunningham161354,9287756.430.6-620-3.00.00
Steve GroganSteve Grogan149352,1764454.914.61936.30.10
Aaron RodgersAaron Rodgers208343,3476765.016.1-1133-3.7-0.10
Daunte CulpepperDaunte Culpepper105342,6525145.225.30110.00.00
John ElwayJohn Elway234333,4077744.414.661320.30.31
Otto GrahamOtto Graham72336823062.29.5000.00
Y.A. TittleY.A. Tittle178339992913.45.6414.00.00
Kordell StewartKordell Stewart99322,6175065.226.4130101813.01.31
Terry BradshawTerry Bradshaw168322,2574445.113.4100.00
Fran TarkentonFran Tarkenton246323,6746755.414.9-1200.00
Roman GabrielRoman Gabriel183301,3043583.67.1-51-5.00.00
Donovan McNabbDonovan McNabb167293,4596165.620.7-758-1.40.00
Josh AllenJosh Allen55281,9453695.335.4121212.00.21
Tom BradyTom Brady312261,0966541.73.5653321.70.20
Jeff GarciaJeff Garcia125262,1404684.617.16116.00.00
Dak PrescottDak Prescott79251,4082864.917.8111211.00.11
Drew BreesDrew Brees287257524981.52.674899.30.31
Bobby LayneBobby Layne175252,4516114.014.0000.00
Billy WadeBilly Wade128241,3343184.210.41000.10
StatMuse has season-level data for rushing touchdowns going back to the 1921 season.