He played on the European Tour in 1998 and 1999, also competing on Europe’s developmental Challenge Tour in 1999.
In 2000, he won the Canadian Tour Order of Merit, before moving to the United States to compete on the Nationwide Tour in 2002. He was successful enough to graduate to the full PGA Tour in 2003, but was unable to retain his card and returned to the development tour from 2004 to 2006.
In 2007 and 2008, he went back to Europe to play on the European and Challenge tours. He returned to the Nationwide Tour (now Web.com Tour) in 2009. At the 2014 Cleveland Open on the Web.com Tour, Alker beat South Africa’s Dawie van der Walt on the 11th playoff hole, a tour record for longest playoff. He finished 20th in the Web.com Tour Finals to earn his PGA Tour card for the 2014–15 season.
In 2016, Alker played in The Open after tying for second in the Final Qualifying event held at the Royal Cinque Ports Golf Club.
In November 2021, Alker won the TimberTech Championship on the PGA Tour Champions in Boca Raton, Florida. With the win, Alker had earned $896,207 in nine senior tournaments after turning 50 years of age in July 2021. This amount was more than he made in his PGA Tour career. Alker continued this form into the 2022 season, recording wins at the Rapiscan Systems Classic and the Insperity Invitational. He also finished runner-up at the Mitsubishi Electric Championship at Hualalai and the ClubCorp Classic; losing in a playoff on both occasions.
In May 2022, Alker won his first senior major championship at the 2022 KitchenAid Senior PGA Championship at The Golf Club at Harbor Shores in Benton Harbor, Michigan. Alker shot a final round 63 to win the championship by three strokes. This was his third win in five starts and fourth in 19 as a senior.