An off-duty NYPD cop with a history of domestic violence and drunk driving was busted Thursday for hitting a woman with his car then driving away from the scene while boozed up, police said.

Brayan Terrazas, 32, was driving westbound on 34th Avenue in Jackson Heights just before 7 a.m. when he went through a red light at 69th Street and allegedly struck a female pedestrian with his 2011 Nissan Rogue, police said.

Terrazas, who is assigned to the Housing Bureau, then drove away, but not before catching the attention of two men, ages 35 and 52, who followed him and called police, cops said.

Officers pulled her over more than a quarter-of-a-mile away, at 62nd Street and Northern Boulevard.

When the 10-year-veteran of the force got out of his car, he was swaying while he was walking, had watery eyes and reeked of alcohol, police sources said.

Meanwhile, the woman who was struck left the scene before cops or EMS showed up, cops said.

Terrazas was charged with leaving the scene of an accident involving an injury, DWI and driving while ability impaired.

He was previously arrested for drunk driving in 2012, police said. He was also busted twice for domestic violence, including an incident in 2016 when he allegedly slapped his girlfriend while she was holding a 3-month-old infant.

He was suspended without pay following Thursday’s arrest, cops said.