Rehnquist was already very successful as a junior. He came in at least the third round in all Grand Slam tournaments . In 1996 he won the Australian Open and was in the final of the French Open , which he lost to Alberto Martín . In July he made his professional debut on the ATP World Tour when he received a wildcard for the individual field in Båstad . At the end of the year he achieved his best placement as a junior with 3rd place.
From 1998 Rehnquist regularly played tournaments on the professional tour, at the beginning of his career mainly on the underclass ITF Future Tour , on which he won a total of three singles and five doubles. The year 2001 began for him with winning a futures title in singles and another final. On the next higher ATP Challenger Tour , he won the individual competition in Hamilton , after he has not yet won a game in his previous appearances. Through these successes he improved in the world rankings , so that he could regularly take part in tournaments of the Challenger Tour. A year later he won his only double title in Burbank at the side of Louis Vosloo . Rehnquist made his Grand Slam debut in 2002 at the US Open . After successfully qualifying, he was eliminated in the first round against Gastón Etlis in three sets. On the Challenger Tour he made it to the semi-finals more and more often, so he reached his best position at the end of the year with 146th place.
In 2003 he achieved his best score in doubles with 345th place, while he moved around 200th place in singles. In September 2004 he did not play a tournament for six months, which is why he fell out of the top 700 in the world rankings. With his third individual title, he improved back to 260th place by 2006. He qualified for the Australian Open for the first time . In the first round he met Radek Štěpánek , then number 20 in the world, against whom he was eliminated in three sets. He took part again regularly in Challenger tournaments, without first getting beyond the quarter-finals. In doubles he made it to the final in Cardiff , in the following period he did not win beyond the second round.
2008 was a successful year for Rehnquist. In Guangzhou he defeated the Thai Danai Udomchoke in three sets in the final and celebrated his fourth challenger title. His greatest success on the ATP World Tour was the quarter-finals in Båstad . After winning the first set, he had to admit defeat to number 2 of the tournament Fernando Verdasco in three sets. The following week Rehnquist won his last title on the Challenger Tour. In Manchester he played his way to the final without losing a set, where he defeated local hero Richard Bloomfield in three sets . This was to be the last great success for him. He qualified again for the Australian Open in 2009 , but had no chance against the top 10 player Andy Roddick and lost 0: 6, 2: 6, 2: 6. On the Challenger Tour he did not get past the quarterfinals, which meant that he could not hold his position in the world rankings. After a defeat in qualifying for the tournament in Båstad , he ended his active career.