Much of Rosenzweig’s early karting career was contested in the United Kingdom, with him competing in Super 1 karting championships. In 2001, Rosenzweig finished fifth in the Cadet Championship, having been outside the top thirty positions the previous season. 2002 saw Rosenzweig step up to JICA karts, again competing in the Super 1 championship, staying there for two seasons with an additional shot at the Andrea Margutti Trophy in 2004.

After a season out in 2005, Rosenzweig moved up to ICA karts for the 2006 season. Rosenzweig contested the Stars of Karting championship in the United States, finishing eighth overall in the championship standings. He also made appearances in the WSK International Series and Italian Open Masters, scoring nine points in both series. Rosenzweig remained in the States to contest the most part of his 2007 karting campaign, claiming both the ICA Florida Winter Tour and the Canadian ICC Championship, and finished runner-up in two other championships – Stars of Karting National and East series – losing out to British racer Scott Jenkins on both occasions. He also finished thirteenth at the SuperNationals event in Las Vegas, Nevada, beating the likes of Raphael Matos and Phil Giebler.

Rosenzweig tested a GP2 car for Super Nova Racing during the mass test at Circuit Paul Ricard in November 2009. He would later join the team for the final two rounds of the 2009–10 GP2 Asia Series, replacing Marcus Ericsson alongside Josef Král.

Rosenzweig made his main series début in the non-championship GP2 Final in 2011 with the Super Nova team. He returned to the series for the penultimate round of the 2012 championship at Monza, replacing Josef Král in the Addax team, alongside Johnny Cecotto Jr..