Weinstein is seeking $US5 million ($A6.9 million) in damages, saying the August 17, 2019 accident in Bedford, New York left him "catastrophically injured and rendered paralysed" with "significant and continuing conscious pain and suffering" from what his lawyer called "severe spine and back injuries".
According to the complaint filed in a New York state court in Manhattan, Weinstein was wearing his seatbelt when the brakes on the 2017 Wrangler failed as he approached the deer, causing a rollover.
Weinstein said the defendant FCA US LLC, now owned by Stellantis, had provided him the "unreasonably dangerous" vehicle in exchange for product placement in one of his films.
Bedford is about 64km north of Manhattan.
"We intend to vigorously defend our product against these claims," Stellantis said in a statement.
Gary Kavulich, a lawyer for Weinstein, disputed press reports suggesting his client was uninjured, saying Weinstein told authorities he was hurt at the time of the accident.
"He is in constant pain, it's debilitating," Kavulich said in a statement, adding that negotiations with FCA to avert a lawsuit "went on for months and months".
Weinstein, 70, is serving a 23-year prison sentence following his February 2020 jury conviction in Manhattan for sexual assault and rape.
A New York state appeals court upheld the conviction on Thursday.
The case remains the highest-profile trial in the MeToo movement against sexual misconduct by prominent men.
Weinstein underwent back surgery in December 2019 and used a walker during the trial.
He is awaiting trial in Los Angeles on other alleged sex crimes from 2004 to 2013, and has pleaded not guilty.Â
Weinstein has denied any non-consensual sexual encounters.
