Körner was born in Vienna. He had a successful career with Rapid Wien between the mid-1940s and 1959. He won seven league titles with the club. He also played for the Austria national team from 1946 to 1958. He played in the 1954 FIFA World Cup, where Austria finished third, and the 1958 FIFA World Cup. He earned 47 caps for his country, scoring 14 goals.