He played junior hockey for the Edmonton Oil Kings from 1971 to 1974. The New York Islanders chose him 129th overall in the 1974 NHL Amateur Draft while the Cincinnati Stingers chose him 18th overall in the 1974 WHA Amateur Draft.
Inkpen turned pro in 1974-75 and played minor pro hockey in the Islanders' system. In 1975-76 he signed with the Stingers and began a four year career in the World Hockey Association (WHA) with five different teams, ending up with the New England Whalers in 1978-79 when the WHA folded.
In the WHA Inkpen played 293 games and scored 13 goals and 76 assists.