Abraham started racing in the 125cc class of the world championship in 2005, riding for Semprucci Cardion Blauer on an Aprilia motorcycle. In 2006 he rode for his father's AB Motoracing team.
250cc World Championship
From 2007 to 2009, Abraham rode in 250cc for AB Motoracing using Aprilia motorcycles.
Moto2 World Championship
In 2010, Abraham and AB Motoracing competed in the new Moto2 class, using RSV and FTR chassis. Abraham took his and his team's first victory in Valencia.
MotoGP World Championship
Abraham and the team stepped up to MotoGP in 2011, having signed a contract with Ducati, he finished the season in fourteenth place in the championship; his best results were a pair of seventh-place finishes at Jerez and Silverstone. The team remained with Ducati for 2012[7] and Abraham finished the season with a best result of 7th at Valencia.
For 2013 Abraham switched to an ART-Aprilia running under CRT regulations, He finished the season in 24th place overall with just 5 points. CRT was restructured as the "Open" class for 2014 and Abraham took part with the new Honda RCV1000R. He obtained the 17th position in the riders' championship. In 2015 Abraham struggled with the Honda RC213V-RS and did not score any points.
Abraham returned to MotoGP in 2017 riding a Ducati for the Pull&Bear Aspar Team. He remained with the team, now called Ángel Nieto Team, for 2018. He raced for Avintia Racing on a Ducati in 2019. His contract was terminated at the end of the season.[8][9]