In 1999, Rumford won the PGA Tour of Australasia's ANZ Players Championship as an amateur, and he turned professional the following year.

Rumford played on the PGA Tour in 2008, after earning his card through qualifying school, finishing the season ranked 149th in the FedEx Cup standings.

In a sudden-death playoff, Rumford eagled the first extra hole to defeat Marcus Fraser and Peter Whiteford.

In the playoff, after both opponents had failed to reach the par-five 18th in two, Rumford fired his approach to within four feet of the hole to set up the eagle and seal victory.

[3] In February 2017, Rumford won the ISPS Handa World Super 6 Perth.