John Wolford has the most rushing yards per game by a rookie quarterback, with 56.0 per game in 2020.

who has the most rushing yards per game by a rookie qb in a season
2020Wolford2012Griffin2018Allen1985Young1961Kilmer1987Fourcade2011Newton2018Jackson2017Watson1968Carter1969Douglass2010McGee2006Young2001Vick1999Delhomme1935Shepherd2002Garrard1987Hold1985Cunningham2019Murray1964Concannon1942Hapes1987Mackey56.054.352.646.646.344.744.143.438.437.937.137.036.836.136.035.434.834.534.234.033.533.032.7
NAMESEASONTMGPRUSH YDS/GRUSH YDSATTRUSH AVGRUSH TDREC YDSRECTRGREC AVGREC YDS/GREC TD
John WolfordJohn Wolford2020LARLAR156.05669.300000.00
Robert Griffin IIIRobert Griffin III2012WASWAS1554.38151206.870000.00
Josh AllenJosh Allen2018BUFBUF1252.6631897.180010.00
Steve YoungSteve Young1985TBTB546.6233405.81000.00
Billy KilmerBilly Kilmer1961SFSF1146.3509965.310000.00
John FourcadeJohn Fourcade1987NONO344.7134197.10000.00
Cam NewtonCam Newton2011CARCAR1644.17061265.614271127.01.70
Lamar JacksonLamar Jackson2018BALBAL1643.46951474.750020.00
Deshaun WatsonDeshaun Watson2017HOUHOU738.4269367.520000.00
Virgil CarterVirgil Carter1968CHICHI737.9265485.54000.00
Bobby DouglassBobby Douglass1969CHICHI1137.1408518.02000.00
Stephen McGeeStephen McGee2010DALDAL237.074135.700000.00
Vince YoungVince Young2006TENTEN1536.8552836.770000.00
Michael VickMichael Vick2001ATLATL836.1289319.310000.00
Jake DelhommeJake Delhomme1999NONO236.072116.520000.00
Bill ShepherdBill Shepherd1935TOT1235.44251433.043348.32.80
David GarrardDavid Garrard2002JAXJAX434.8139255.620000.00
Mike HoldMike Hold1987TBTB234.56979.90000.00
Randall CunninghamRandall Cunningham1985PHIPHI634.2205297.10000.00
Kyler MurrayKyler Murray2019ARIARI1634.0544935.840000.00
Jack ConcannonJack Concannon1964PHIPHI433.5134168.41000.00
Merle HapesMerle Hapes1942NYGNYG1133.0363953.8379107.97.22
Kyle MackeyKyle Mackey1987MIAMIA332.798175.82000.00
Russell WilsonRussell Wilson2012SEASEA1630.6489945.240000.00
Fred EnkeFred Enke1948DETDET1230.4365744.90616.00.50
StatMuse has season-level data for rushing yards per game going back to the 1932 season.

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