Cam Newton scored the most rushing touchdowns by a quarterback in his first 3 seasons, with 28 touchdowns.

which qb has the most rushing td in their first 3 seasons
NewtonAllenJacksonPrescottGroganMurrayStewartWatsonKempLujackBradshawGrahamLuckTebowSanchezCulpepperPeeteWilsonGarciaZornKilmerYoung28251918161515141414131312121212121111111110
NAMEGPRUSH TDRUSH YDSATTRUSH AVGRUSH YDS/GREC YDSRECTRGREC AVGREC YDS/GREC TD
Cam NewtonCam Newton48282,0323645.642.3331133.00.70
Josh AllenJosh Allen44251,5623005.235.5121212.00.31
Lamar JacksonLamar Jackson46192,9064826.063.20020.00
Dak PrescottDak Prescott48189441895.019.70010.00
Steve GroganSteve Grogan41168311515.520.3000.00
Kyler MurrayKyler Murray32151,3632266.042.60000.00
Kordell StewartKordell Stewart48151,1402255.123.8130101613.02.71
Deshaun WatsonDeshaun Watson38141,2332175.732.46116.00.21
Jack KempJack Kemp32143421003.410.7000.00
Johnny LujackJohnny Lujack3314571866.617.316116.00.50
Terry BradshawTerry Bradshaw41138261435.820.1000.00
Otto GrahamOtto Graham36133041322.38.4000.00
Andrew LuckAndrew Luck48129051894.818.90000.00
Tim TebowTim Tebow35129891975.028.30010.00
Mark SanchezMark Sanchez47123141033.06.70000.00
Daunte CulpepperDaunte Culpepper28128921635.531.90110.00.00
Rodney PeeteRodney Peete27126361056.123.6000.00
Russell WilsonRussell Wilson48111,8773086.139.1171117.00.40
Jeff GarciaJeff Garcia45118991894.820.00000.00
Jim ZornJim Zorn40116771365.016.9000.00
Billy KilmerBilly Kilmer27116741195.725.0000.00
Vince YoungVince Young33109741845.329.50000.00
Michael VickMichael Vick28101,3211847.247.216000.60
Steve McNairSteve McNair29108811436.230.4000.00
Scott HunterScott Hunter351090511.82.6000.00
StatMuse has season-level data for rushing touchdowns going back to the 1921 season.

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