Carney was a member of the Illini men's basketball team from 1920 to 1922. He established the single-season, Big Ten Conference record with 60 field goals during the 1921 Big Ten season. He was selected as All-American basketball player in both 1920 and 1922, becoming the first Big Ten athete to receive All-American honors in both football and basketball. He was named Helms FoundationCollege Basketball Player of the Year in 1922. He was posthumously honored in 2005 by being chosen for the Illinois All-Century basketball team.