Parnell was born in Port Elizabeth in Cape Province in 1989. He attended Grey High School in his home town, leaving in 2007. He studied Human Resource Management at Nelson Mandela Metropolitan University in Port Elizabeth.

Parnell made his first-class cricket debut for Eastern Province in October 2006, at the age of seventeen, against South Western Districts scoring 17 and taking one wicket. In his second first-class match, he recorded figures of four for seven, and, in only his fifth first-class match, he took a hat-trick against Western Province: all three batsman were bowled. He was described as “the most talked about cricketer to hit the first-class scene for some time."

In 2008 Parnell was awarded the Coca-Cola Khaya Majola U19 Player of the Tournament and the CSA U19 Cricketer of the Year while representing Eastern Province.

County cricket

At the start of the 2009 season Parnell was signed as an overseas player by Kent County Cricket Club on a six-week contract, serving as a replacement for Stuart Clark. On his county debut against Essex he took 4/78 in the first innings and top scored with 69 in the second, his maiden first-class fifty, going on to better this score in Kent's next County championship match, against Glamorgan with an innings of 90. Parnell left Kent to join up with South Africa ahead of the 2009 World Twenty20 but after the tournament he returned for a further five weeks. Though returning to South Africa after his second spell ended, Parnell was cleared by Cricket South Africa to return to Kent and played for the county on the competition's finals day.

In 2011 Parnell played for Sussex County Cricket Club for the second half of the season although "he struggled for fitness and form" during his spell with the county. In 2015 he played for Glamorgan in eight matches in the 2015 NatWest t20 Blast group stages before joining South Africa on their tour of Bangladesh. Parnell missed the first two matches of his planned ten with Glamorgan due to a groin injury.

Parnell joined Kent again in April 2017 for the first part of the 2017 season. He was available for the first weeks of the 2017 County Championship and 2017 Royal London One-Day Cup matches until South Africa began their tour of England in May.