He played for the University of Michigan from 1973 to 1977. He was chosen 85th overall by the Los Angeles Kings in the 1976 NHL Amateur Draft and 102nd overall by the Calgary Cowboys in the 1976 WHA Amateur Draft. Palmer opted to join the Kings and made it to the NHL in his first pro season, 1977-78. He was a Kings' regular for the next two seasons but by 1981 his career was on a downslide. He spent most of the 1980-81 and 1981-82 seasons in the minor pros. In the NHL Palmer played in 320 games and scored 9 goals and 101 assists.