A right-handed batsman and wicket-keeper, Wessels has played for Marylebone Cricket Club, Northamptonshire and Nottinghamshire, and also for the Mid West Rhinos in Zimbabwe and the Sydney Sixers in Australia.

In 2004, Wessels joined the staff at Northamptonshire County Cricket Club where he impressed in the second eleven producing several noticeable scores.

On 7 November 2008, Wessels signed a contract extension along with fellow Northamptonshire wicket keeper Niall O'Brien, keeping Riki at the club until 2010.

Wessels signed for Nottinghamshire County Cricket Club for the 2011 season, where he plies his trade as a specialist batsman.

He was signed as a specialist batsman by the Sydney Sixers in the 2014–15 Big Bash League tournament in Australia.