Michael Vick has rushed for the most career yards by a quarterback, with 6,109 yards.

who had the most qb rush yards career
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VickNewtonCunninghamWilsonYoungTarkentonJacksonMcNairMcNabbElwayRodgersRoteHarbaughLandryDouglassCulpepperFitzpatrickStewartSmithLayneGannonBrunell6.1k5.6k4.9k4.7k4.2k3.7k3.7k3.6k3.5k3.4k3.4k3.1k2.8k2.7k2.7k2.7k2.6k2.6k2.6k2.5k2.4k2.4k
NAMEGPRUSH YDSATTYPCRUSH YDS/GRUSH TDREC YDSRECTRGAVGREC YDS/GREC TD
Michael VickMichael Vick1436,1098737.042.7361220.50.00
Cam NewtonCam Newton1485,6281,1185.038.075683322.70.51
Randall CunninghamRandall Cunningham1614,9287756.430.635-620-3.00.00
Russell WilsonRussell Wilson1584,6898465.529.72320445.00.11
Steve YoungSteve Young1694,2397225.925.1432201.00.00
Fran TarkentonFran Tarkenton2463,6746755.414.932-1200.00
Lamar JacksonLamar Jackson583,6736156.063.3210020.00
Steve McNairSteve McNair1613,5906695.422.3374114.00.00
Donovan McNabbDonovan McNabb1673,4596165.620.729-758-1.40.00
John ElwayJohn Elway2343,4077744.414.63361320.30.31
Aaron RodgersAaron Rodgers2133,3726854.915.834-1133-3.7-0.10
Tobin RoteTobin Rote1493,1286354.921.03728214.00.21
Jim HarbaughJim Harbaugh1772,7875615.015.718-820-4.00.00
Greg LandryGreg Landry1462,6554306.218.221000.00
Bobby DouglassBobby Douglass912,6544106.529.222-21-2.00.00
Daunte CulpepperDaunte Culpepper1052,6525145.225.3340110.00.00
Ryan FitzpatrickRyan Fitzpatrick1662,6255744.615.821-333-1.00.00
Kordell StewartKordell Stewart992,6175065.226.432130101813.01.31
Alex SmithAlex Smith1742,6045804.515.015-733-2.30.00
Bobby LayneBobby Layne1752,4516114.014.025000.00
Rich GannonRich Gannon1572,4495214.715.621-321-1.50.00
Mark BrunellMark Brunell1932,4215134.712.5150000.00
Josh AllenJosh Allen612,3254225.538.131121212.00.21
Colin KaepernickColin Kaepernick692,3003756.133.3130000.00
Roger StaubachRoger Staubach1312,2644105.517.320-131-13.0-0.10
StatMuse has season-level data for rushing yards going back to the 1932 season.