Dylan Jason Syer, who began working for the Jumanji actor in 2015, is accused of making unauthorised purchases using Hart's credit cards.
He is alleged to have racked up the payments between October 2017 and February 2019.
The 29-year-old has been charged with grand larceny, criminal possession, identity theft and scheme to defraud.
If convicted, Mr Syer, from Long Island City in New York, faces up to 25 years in prison. He is due to return to court on 17 February.
