Armstrong began karting in 2010 and began winning major titles from 2011 on wards. During karting, Marcus graduated to single seaters in 2014 while in the 2014-15 season of New Zealand Formula Ford Championship. In the following year, he diversified his karting with stints in BRDC British Formula 3 and the two Formula Renault 2.0 series. In the November of 2016, Armstrong was among five drivers who were invited to join the Ferrari Driver Academy and soon became confirmed as a member. In that same month, he was confirmed to race in the Toyota Racing Series with M2 Competition where he finished fourth, taking home three wins.
In 2017, Marcus joined Prema Powerteam to race in the ADAC F4 and the Italian F4 Championships where he claimed seven wins across both series, finishing as runner up in the ADAC F4 and becoming the Italian F4 Champion. He soon returned to the Toyota Racing Series for the 2018 season and continued his journey with Prema, graduating to the FIA Formula 3 European Championship. He managed to claim fifth in the championship, racing alongside his fellow Ferrari Juniors, Robert Shwartzman and Guanyu Zhou. Armstrong competed in the season ending Macau Grand Prix, placing ninth.
FIA Formula 2
For the 2019 season, Marcus reunited with both M2 Competition and Prema. During the Toyota Racing Series, he took five victories but missed out on the title in the season ending New Zealand Grand Prix. In the FIA Formula 3 Championship, Armstrong a feature race victory at Sochi, two back to back sprint race wins at Spa-Francorchamps and the Hungaroring while consistently receiving podium and point finishes to place as runner up alongside teammate Robert Shwartzman. He returned to the Macau Grand Prix with SJM Theodore Racing by Prema and finished eight overall after starting from seventeenth on the grid.
November 28th 2019, ART Grand Prix announced that Armstrong would graduate to compete in the FIA Formula 2 Championship, becoming one of the rookies to race this season.