Rabat began racing professionally in 2005, debuting in the 125cc Valencian Grand Prix with Team BQR as a wildcard rider. In 2006, he competed as a wildcard in the Spanish rounds at Jerez and Barcelona with BQR, and later replaced Aleix Espargaró from round 8 for the remainder of the season.
In 2007, Rabat joined the Repsol Honda 125cc works team, finishing 11th in the championship behind teammate Bradley Smith. He remained with Repsol in 2008, now with KTM bikes, and finished behind Marc Márquez in the standings despite starting three more races. Rabat returned to BQR, under the Blusens name and using Aprilia motorcycles, in both 2009 and 2010.
Rabat moved up to the Moto2 class in 2011 with BQR, finishing 10th overall as a rookie. He switched to Pons Racing for 2012, achieving 7th place in the championship. His breakthrough year came in 2013, recording a second-place finish at the Grand Prix of the Americas and his first pole position and race win at the Spanish Grand Prix.
For the 2014 Moto2 season, Rabat moved to the Marc VDS team and won the opening race at Qatar. He secured a total of seven wins and seven podiums throughout the season, culminating in the World Championship title – the first for the Marc VDS team. Remaining in Moto2 for 2015, Rabat won races at Mugello, Aragon, and Valencia, but ultimately finished third behind Johann Zarco and Álex Rins.
Rabat moved up to MotoGP in 2016 with EG 0,0 Marc VDS on a satellite Honda bike, recording his first top-ten finish in Argentina. He remained with Marc VDS for 2017, managing only one top-ten finish in the final race of the season and finishing 19th in the rider’s championship with 35 points.
For 2018, Rabat returned to Reale Avintia Racing, where he suffered a major crash at the British Grand Prix, sustaining a triple fracture to his right leg after being hit by Franco Morbidelli’s out-of-control machine, contributing to the race’s cancellation. He missed the remaining seven races of the 2018 season and finished 19th in the rider’s championship with 35 points. He returned in 2019 with Avintia, outscoring teammate Karel Abraham and finishing 20th in the championship. In 2020, partnered with Johann Zarco under the Esponsorama Racing banner, Rabat had a difficult year, finishing 22nd with 10 points. Esponsorama bought out his contract early at the end of the season.
In 2021, Rabat returned to the MotoGP grid as a replacement rider for the injured Jorge Martín with Pramac Racing. Later in 2021, he joined Kawasaki Puccetti Racing in the Superbike World Championship, and remained with the team through 2024. In March 2021, Rabat also announced he would ride a Ducati Panigale V4 R with the Barni Racing Team in World Superbike, but parted ways with the team before the season’s end. He joined the Yamaha Motoxracing WorldSBK Team in 2025, before moving to Petronas MIE Racing Honda Team mid-season to replace the injured Tarran Mackenzie.
Beyond Grand Prix racing, Rabat competed in the ESBK Spanish Superbike Speed Championship with Honda Laglisse in 2022, and participated in the British Superbike Championship with TAG Racing Honda at Thruxton, and later with McAms Yamaha, achieving a 10th-place finish in Race 3 at Snetterton in 2023. He also competed in MotoE with Prettl Pramac MotoE in 2023.
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