West Midlands Police said officers believe the 40-year-old may have posed as a taxi driver in the city before the incident which happened in the early hours of July 10.
The investigation team is appealing for information after reports that a man posing as a taxi operator in the city centre, Digbeth and Perry Barr areas approached lone women late at night offering lifts home, alcohol and drugs.
The force said a 40-year-old man has been charged with rape and other sexual offences in relation to the matter.
In a statement it said: “We are appealing for any other potential victims or witnesses of similar incidents to contact us. We continue to support the woman and our investigation is still very much ongoing.”
The man, who has not been named, has been remanded in custody.
Anyone with information should contact the force website via its Live Chat service or telephone 101.
*Those affected by this story are advised to contact The Survivors Trust helpline on 08088 010818.