Rinne started her racing career in karting and managed to beat future Formula One drivers Mika Häkkinen, Mika Salo and Jyrki Järvilehto on multiple occasions. She won the Finnish Karting Championship in the 85cc class in 1979, ahead of Häkkinen. In 1980, she finished second behind Salo and ahead of Häkkinen who was fourth. She battled with Häkkinen again in 1981, and this time finished second in the series with Häkkinen becoming the champion. The next year Rinne won the series again and Häkkinen had to settle with second place. In 1983, she also finished first in the championship but was disqualified from the last race due to illegal fuel. Thus the title went to Häkkinen. She was also given a personal one-year ban from racing, which eventually ended her promising career in karting.
Despite her success on four wheels, Rinne decided to switch to motorcycles and debuted in the Road Racing World Championship, now known as MotoGP, in 1988. With her Honda bike she qualified second for the 125cc class GP at Hockenheim in 1989 and managed to lead the race for a while. She eventually finished seventh bettering her earlier eighth place at Assen. This was to remain her best ever result, as she got into a bad accident at Paul Ricard. While recovering from the accident, she got a bad surprise in the form of a letter from Bernie Ecclestone, who at the time decided who drives in the series and who doesn't. The letter said that she is not qualified to drive in the series next season. This ended her career at top-level and frustrated Rinne couldn't understand "how a man, who doesn't even know her decides to end her racing career".