Prior to joining the Formula Renault series, Stöckinger won titles and honors from international derbies such as the Formula BMW Pacific 2008 Championships, the Senior Rotax Max World Finals 2007, the Asian Karting Championship 2006, the Junior Rotax Max-World Finals 2005 and the Philippine Shell Super Karting Series 2002. He participated at the 2008 Formula BMW Europe season - the championship's maiden season after the merger of the British and German series — as a guest driver, racing at the Hungaroring, Valencia Street Circuit and at the Circuit de Spa-Francorchamps.
Formula Renault (2009–2010)
Stöckinger made his debut at the UK championship in 2009 at 18 years of age, joining other newcomers including Harry Tincknell, Matias Laine and Will Stevens. He arrived 20th on his debut at Brands Hatch and eventually finished 25th in the championship with 56 points. His best result was an eleventh place at round eight at Oulton Park. The following season began at Thruxton on 3 April 2010 and will end on 10 October at Brands Hatch, after twenty rounds held in England, and for the first time since 2006, Scotland. After arriving 10th in his first race of the year, the Filipino-Swiss driver was able to finish third at Rockingham Motor Speedway, his best result ever in two seasons. At the Croft Circuit he started from pole and finished the race first, becoming the first Filipino to have won a formula race in Europe. The performance was then followed by a second place in the same circuit, behind Lewis Williamson.
The following year, Stöckinger moved to the GP3 series, where he suited up for Atech CRS Grand Prix in the 2011 GP3 Series season. Going into his second year in the GP3 Series, the Filipino was assessed by Status Grand Prix during their autumn tests. Stöckinger was regularly featured in the Top 5 of the time sheets at Barcelona, Valencia and Jerez tests, and impressed the team with his performances. In February 2012, Stöckinger left Atech GP and signed to join Status Grand Prix for the 2012 GP3 Series season. Stöckinger collected his first win in the 2012 GP3 Series at Monaco and set his first pole position and the fastest lap of the race.
Formula Renault 3.5 Series (2013-2015)
He became a member of the Lotus F1 Team in February 2013, serving as one of seven junior team drivers. Stöckinger and the other six young drivers will be supported by Lotus in all areas such as driving skills, physical fitness, health and nutrition, social and mental development, business ethics and principals, as well as PR training as a preparation for their future careers. It was confirmed that Stöckinger will stay and drive for Lotus F1 on 2014 Formula Renault 3.5 season alongside newly recruited Matthieu Vaxivière of France and former French F4 Champion.
GP2 Series (2015)
On 5 March2015, it was confirmed Stöckinger would reunite with Status as one of their drivers in the 2015 GP2 season.
, Stöckinger has been romantically involved with Miss Universe 2015Pia Wurtzbach. Stöckinger is a practising Catholic. He has twin daughters with model Kit Barraquias.