Robinson was born in Des Moines, Iowa as Eileen "Shawna" Jade, the youngest of five children of Richard "Lefty" Robinson, an amateur diesel truck racer, and his wife Lois, who had also competed in auto racing. She grew up in a racing household, driving minibikes, motorcycles, and snowmobiles as a child. After graduating from Saydel High School in 1983, she began racing semi-tractors at Toledo Speedway, finishing second in her debut. She won 30 feature races and moved into the GATR (Great American Truck Racing) Truck Series, winning the Milwaukee Mile Bobtail 100 at Milwaukee Mile to become the first woman to win a GATR points-scoring race on a superspeedway. She was voted the 1984 GATR Rookie of the Year. She subsequently competed in truck races in France at Paul Ricard and finished second in the 1986 Grand Prix of Trucks in Mexico City.
Robinson began competing in the Charlotte/Daytona Dash Series in spring 1988. On June 10, 1988, she won the AC Delco 100 at Asheville-Weaverville Speedway — becoming the first woman to win a top-level NASCAR Touring Series race, starting thirteenth and leading with seven laps remaining. She finished third in the drivers' championship and won the series Rookie of the Year. In 1989, she claimed the first pole position by a woman in any NASCAR series at I-95 Speedway, then won the race at Myrtle Beach Speedway from that front-row start and also took victory at Lanier National Speedway. She finished third in the Dash Series championship for a second consecutive season and retained the series Most Popular Driver award for the second year running. Her two Dash Series wins in 1989 were not equaled by another woman in a major NASCAR touring race until 29 years later.
Robinson moved to the NASCAR Busch Series in 1991, driving the No. 77 Huffman Racing Buick. She faced immediate financial difficulties, running sponsorless in her first appearances. Over the following seasons she competed with multiple teams including Silver Racing, Pharo Racing, Laughlin Racing, and Ferree Racing. Her most significant Busch Series achievement came in 1994 when she qualified second and then captured the first pole position by a woman in the Busch Series in the Busch Light 300 at Atlanta Motor Speedway. She achieved her best points finishes of 23rd in 1993 and was runner-up in the 1992 Rookie of the Year standings behind Ricky Craven. She retired from racing in 1995 during the early stages of pregnancy, declining a test opportunity at Daytona International Speedway.
Robinson returned to racing in 1999 in the ARCA Bondo/Mar-Hyde Series for car owner James Finch, finishing second at Daytona in her debut — the best result by a woman in the series at that time. For the 2000 season, Kranefuss-Haas Racing fielded her full-time in ARCA, making her the first woman to compete full-time in an American national stock car racing series. She took top-ten finishes in half the races she entered, set a track record at Michigan International Speedway, led laps at Toledo Speedway — becoming the first woman to lead in the ARCA Series — and finished sixth in the championship standings, the highest final-points position achieved by a woman in an American national oval series to that point.
In 2001, Robinson made her NASCAR Winston Cup debut in the No. 84 Michael Kranefuss Racing Ford Taurus at Michigan International Speedway, becoming the first woman to start a Cup race since Patty Moise in 1989. She moved to BAM Racing for 2002 and started the Daytona 500 from 36th position, finishing 24th after avoiding a pit-road collision with Bobby Labonte — becoming the second woman to start the race. Sponsorship shortfalls hampered her season and she finished 52nd in the championship. She made three Craftsman Truck Series starts in 2003 for Mike Starr Racing with an all-women pit crew, and continued sporadic appearances through 2005 before retiring from competition.
After leaving racing Robinson focused on her interior design and furniture business, founding a company called Happy Chairs in the Matthews area of Charlotte. In March 2014 she was diagnosed with stage three breast cancer; she received treatment including chemotherapy and radiation, and later entered remission, completing final radiation therapy in September 2015. Dale Earnhardt Jr. and Kelley Earnhardt Miller ran fundraising events to assist with her medical bills.
Robinson is recognized as a significant figure in breaking gender barriers in American motorsport. She has described herself as carrying forward the work of Janet Guthrie in "opening doors for a lot of women" in racing. The Iowa Senate honored her with a resolution in March 2002, and her record of firsts — first woman to win a NASCAR touring race, first Busch Series pole by a woman, first to race full-time in a national stock car series — marks a lasting contribution to the sport.