Shaw was born 10 miles east of Des Moines, Iowa in Mitchellville on March 28, 1899 to Tim and Margaret Shaw, who were cattle ranchers. He was one of five children along with brothers Bill, Jim, and John and a sister, Mary. When Shaw was 10, the family moved to Stuart, Iowa, where high school football had been abolished because of a fatality. He played only four games as a prep after the sport was brought back in 1917, his senior year.