Rabat made his world championship debut as a wildcard rider at the final race of the 2005 season in Valencia with team BQR. For 2006 he rode as a wildcard in the Spanish rounds before replacing Aleix Espargaro mid-season from round 8 onward. In 2007, Rabat was given a full works seat with Repsol Honda in the 125cc class, partnering Bradley Smith and finishing the season in 11th place. When Honda departed the 125cc class in 2008, the Repsol team switched to KTM, and Rabat was retained alongside a young Marc Marquez; despite starting three more races, he finished behind Marquez in the standings. He spent 2009 and 2010 back at BQR under the Blusens banner on Aprilia machinery.
Rabat moved to the Moto2 class in 2011 with BQR and finished a creditable 10th in his rookie season. A switch to Pons Racing in 2012 produced a 7th-place championship finish, and in 2013 his form surged dramatically. He achieved a pole position at the Spanish Grand Prix, won that race by over four seconds, and added further victories at the Indianapolis and Malaysian Grands Prix, signalling he was ready to contend for the title.
For 2014, Rabat joined the Marc VDS Racing Team and delivered a comprehensive championship campaign. He won the season-opening race at Qatar and continued to add victories across the season — six more wins and seven further podiums — only missing the podium in four races all year. He finished the Malaysian Grand Prix in third place and was crowned 2014 Moto2 World Champion with a total of 346 points, the first title for the Marc VDS team.
Staying in Moto2 for 2015 to attempt back-to-back titles, Rabat eventually finished third in the standings behind Johann Zarco and Alex Rins, taking wins at Mugello, Aragon, and Valencia but unable to defend his championship.
Rabat stepped up to MotoGP in 2016 with EG 0,0 Marc VDS on a satellite Honda. His five full MotoGP seasons were marked by modest results and limited competitiveness, with a top finish of ninth in Argentina in 2016 and only single top-ten finishes in subsequent seasons. He moved to Reale Avintia Racing in 2018, and at that year's British Grand Prix was struck by the crashed machine of Franco Morbidelli at Stowe corner, sustaining a triple fracture to his right leg that caused him to miss the final seven races of the season. He returned for 2019 and 2020 with the rebranded Esponsorama Racing squad before losing his seat early, and made a brief return to MotoGP in 2021 as a replacement for the injured Jorge Martin at Pramac Racing.
Rabat joined the Superbike World Championship in 2021 with the Barni Racing Team on a Ducati, though the arrangement ended before the season was complete. He subsequently raced with Kawasaki Puccetti Racing through 2024, and joined the Yamaha Motoxracing WorldSBK Team at the start of 2025 before switching mid-season to the Petronas MIE Racing Honda Team as a replacement for the injured Tarran Mackenzie. He also competed in MotoE with Pramac Racing in 2023, appeared in the British Superbike Championship as a temporary replacement rider in 2022, and raced in the ESBK Spanish Superbike Championship.
Rabat's 2014 Moto2 world title remains the centrepiece of his career, representing the culmination of a determined progression through the junior classes. His longevity at MotoGP level despite limited machinery, and his continued racing activity across multiple championships into his mid-thirties, reflect an enduring competitive spirit. The 2018 Silverstone crash, one of the most serious incidents of that era, underscored the physical dangers of motorcycle racing at the highest level.