Steinhausen made his debut in motorcycle racing in 1961. After some early incidents, he moved to the sidecar class in 1964, influenced in part by his friendship with four-time Sidecar World Champion Max Deubel. Deubel recognised Steinhausen's ability and provided him with one of his sidecars, giving the young German a meaningful platform from which to develop.
Steinhausen spent several years building his competitive record in national and international sidecar racing before entering the FIM Grand Prix World Championship consistently. His early Grand Prix outings produced a steady accumulation of experience rather than breakthrough results, though he showed competitive pace that justified his continued presence at the top level.
Beginning in 1972, Steinhausen made a decisive technical choice that would shape his championship years. Rather than continuing with the established BMW flat-twin engines that had powered the majority of front-running sidecars through the 1960s, he adopted König power units — four-cylinder two-stroke engines originally developed for powerboat racing. The König engines allowed Steinhausen to build a lower, more aerodynamically efficient sidecar chassis, and the combination proved increasingly competitive as the season progressed.
In his 1972 world championship debut, contested in partnership with passenger Werner Kapp, Steinhausen finished tenth overall, with a best result of fourth place at the Austrian Grand Prix. The following season, sharing duties between Karl Scheurer and Erich Schmitz as passengers, he improved to sixth in the world standings and claimed his first Grand Prix podium — a third place at the Sidecar TT.
For the 1974 season, Steinhausen worked with specialist Dieter Busch to build a new chassis. The improved package delivered his first Grand Prix victory, at the Belgian round, and he finished fourth in the world championship, again using two passengers — Scheurer and Josef Huber — across the season.
The 1975 season brought Steinhausen his first world title. Racing with passenger Josef Huber, he won three Grands Prix — Austria, the Isle of Man TT, and Belgium — to claim the Sidecar World Championship. The 1975 title was also historically significant as the first world championship won by a two-stroke powered sidecar, marking the end of BMW's monopoly on championship success in the class.
In 1976 Steinhausen retained his title, winning the same three Grands Prix as the previous year — Austria, the Sidecar TT, and Belgium — to confirm the championship in consecutive seasons. His TT victory that year added to his growing record at the Isle of Man.
The 1977 season saw Steinhausen widely regarded as the favourite for a third consecutive title, but recurring engine problems undermined his campaign. From the French Grand Prix onwards he switched from König to Yamaha power and took on Wolfgang Kalauch as his new passenger. Despite the disruption the pair ended the season fourth overall, with a win at the Czechoslovakian round and a notable lap record at the Belgian Grand Prix of 200.520 km/h.
Despite winning his third Isle of Man Sidecar TT, Steinhausen had a difficult 1978, finishing fourteenth in the world standings. The 1979 season saw him contest the B2A category classification, finishing second behind Swiss racer Rolf Biland. He continued racing into the 1980s, winning two German sidecar national titles in 1986 and 1987 before concluding his competitive career in late 1989.
After retiring from racing, Steinhausen became an entrepreneur, building a trucking business. His son Jörg Steinhausen continued the family involvement in sidecar racing. Rolf Steinhausen's legacy rests on two world championships, three Isle of Man TT wins, and a technical innovation — the adoption of König two-stroke engines — that permanently altered the competitive landscape of Grand Prix sidecar racing. He remains one of the central figures of the transition era between BMW dominance and the multi-manufacturer competition that followed.