A woman in her 30s suffered serious injures in the attack in Longlands Street at about 7pm on Saturday, March 2.
The police have said the injuries are not thought to be life-threatening.
A 58-year-old man from Bradford was charged and remanded in custody on Sunday, March 3.
A bronze-coloured Ford Fiesta with an '18 registration plate is believed to be linked to the assault.
The vehicle is believed to have links to the Wyke area and the city centre.
Police have asked anyone with information to contact Bradford District CID on 101, quoting crime reference 13190112858.