Sinkwich gained early recognition as a star athlete at Youngstown’s Chaney High School. He went on to the University of Georgia to play under coach Wally Butts where he was a two-time All-America selection. In 1941 he led the nation in rushing yards with 209 carries for 1,103 yards. He set the NCAA single-season total offense record of 2,187 yards and led the Bulldogs to an 11–1 season in 1942, capturing the Southeastern Conference championship and a victory over UCLA in the 1943 Rose Bowl. That same year, the Washington D.C. Touchdown Club honored Sinkwich as “back of the year”, and he was overwhelmingly voted the “Number 1 athlete for 1942” in the annual poll by the Associated Press over second-place finisher Ted Williams of the Boston Red Sox, a year in which Williams hit for baseball’s triple crown.

The 1942 season was Sinkwich’s first year of backfield-mate Charley Trippi. Georgia defeated Florida 75–0, the worst defeat in the history of Florida football. Sinkwich played with a broken jaw and kicked a field goal in a 19–3 defeat of Florida in 1941.

In his three-year college career, Sinkwich rushed for 2,271 yards, passed for 2,331 yards, and accounted for 60 touchdowns (30 rushing and 30 passing). Sinkwich earned his Bachelor of Science in Education (B.S.Ed.) from the university in 1943 and was a member of the Pi Kappa Alpha Fraternity.<

After his collegiate career, Sinkwich joined the United States Marine Corps; however, due to his flat feet he received a medical discharge and proceeded to play with the Detroit Lions, who had selected him first overall in the 1943 NFL Draft. In Detroit, he earned All-Pro honors in 1943–1944, as well as being named as NFL MVP in 1944.

After his two years in Detroit, Sinkwich served in both the United States Merchant Marines and the United States Army Air Forces, but a knee injury received while playing for the Second Air Force Superbombers football team in 1945 hampered his playing career when he returned to professional football in 1946 and 1947. He coached the semi-professional Erie (PA) Vets football team in 1949. Sinkwich was inducted into the College Football Hall of Fame in 1954.

According to an article Sinkwich wrote in 1988, he grew to appreciate the value of competitiveness on the streets of Youngstown’s west side. “I learned early in neighborhood pickup games that I had the desire to compete”, he wrote. “When people ask why I succeeded in athletics, I always tell them that I didn’t want to get beat”.