He played professionally from 1943 until 1945 for the Chicago Cardinals and was included on their merged team with the Pittsburgh Steelers, known as "Card-Pitt", in 1944.
Prior to his professional career, Robnett played college football for the Texas A&M Aggies, earning consensus All-American honors as a senior.
In 1940 after helping the Aggies to two straight Southwest Conference titles and the 1939 national championship, Robnett finished ninth in the 1940 Heisman Trophy balloting while being one of the primary blockers for Heisman runner-up John Kimbrough.
Robnett's performance at Texas A&M helped make him a sixth-round draft choice by the Cardinals in 1941.
[1] Marshall was also the older brother of Ed Robnett, who also played at Texas A&M.