Corsi made his Grand Prix debut in the 125cc class at Mugello in 2002, riding a Honda RS125R and finishing 22nd. From 2003 he became a regular in the world championship, joining the Kopron Team Scot alongside Andrea Dovizioso. He scored nine point-scoring finishes in 2003 and improved in 2004, taking his first podium with a third place in Japan while Dovizioso won the race outright. Both riders moved to 250cc together in 2005, Corsi finishing fourteenth in the standings.
Corsi returned to 125cc in 2006 with the Squadra Corse Metis Gilera squad, managing only two fourth places as his best results. A move to Skilled Racing Team in 2007 brought his first Grand Prix victory at the Turkish Grand Prix in Istanbul, and he ended the season sixth overall with 168 points — both career highs to that point.
The 2008 season with the Jack & Jones WRB team on a factory-spec Aprilia RSA 125 appeared set to deliver the world championship. Corsi won at Jerez, Estoril, Mugello, and Valencia, and added three third-place finishes, finishing with 225 points. He ultimately came up four wins and 39 points short of Mike Di Meglio's Derbi, ending as 125cc runner-up. A final season in the class in 2009 with Fontana Racing produced only two podiums and 81 points, placing him eleventh.
Corsi stepped up to the new Moto2 class in 2010 with Team JiR. He scored the team's first podium in the intermediate category with a third place at Le Mans and added another podium at Mugello, ending the season fifth overall with 138 points. Riding for IodaRacing Project in 2011 and 2012, he repeated the pattern of two podiums per season before results declined in 2012.
He joined Forward Racing in 2013 for what became a multi-year spell. In 2013 he took a second place in Germany. A strong start to 2014 — including three consecutive fifth-place finishes and a second place at Le Mans — was derailed when he suffered a serious open fracture of the left ulna at Silverstone, requiring a four-hour operation at the John Radcliffe Hospital in Oxford. Despite missing six races, he still finished seventh in the championship with 100 points.
Corsi subsequently rode for Speed Up Racing in 2016 and 2017, scoring podiums at Qatar and Le Mans in 2016 but also accumulating a reputation for on-track incidents, including a contact with Takaaki Nakagami in Austin and Brno that drew a ride-through penalty for dangerous riding. He moved to Tasca Racing for 2018 and 2019, where results continued to decline; poor performances in 2019 led to his replacement by Mattia Pasini mid-season.
Corsi rejoined MV Agusta Forward Racing for the 2020 season and remained through 2022. The 2021 campaign started with a high-side at Qatar that caused a compound fracture in his left wrist. After recovering, he started his 300th career race at Misano, becoming only the fifth rider after Loris Capirossi, Valentino Rossi, Andrea Dovizioso, and Thomas Lüthi to reach that mark. His final qualifying session in Valencia produced an unexpected pole position — his first in nearly nine years — but a technical failure prevented him from starting from the front of the grid. In 2022, his final Grand Prix season, he failed to score a point, and MV Agusta's tension with new owner KTM left the team uncompetitive throughout the year.
After his Grand Prix career ended, Corsi competed in the Supersport World Championship in 2024, including wildcard appearances for Forward Racing in Moto2. Upon the conclusion of that season, he was appointed team director at Forward Racing, transitioning from racer to manager.
Corsi's career represents one of the longest runs of sustained Grand Prix participation in the sport's modern era. While a 125cc world title eluded him — most painfully in 2008 — his longevity, more than 300 starts, and the record of his contemporary rivalries with Dovizioso, Di Meglio, and Nakagami make him a significant figure in the 125cc and Moto2 eras. His five all-time ranking in career starts underscores a durability that few riders have matched.