It happened after the 20-year-old got into the vehicle in King Street at around 5am, which took her to Chapel Close off the A6 Barton Road.
Police, who say the woman escaped but was extremely shaken, are keen to speak to anyone who may have seen or heard anything within Chapel Close, or knows the driver.
Among those who may be able to help was a woman who was walking her dog along the A6, near its junction with Warden Hill Road, and enquired after the victim’s welfare.
DI Zara Brown, investigating, said: “It is also possible someone recalls seeing the victim getting in the vehicle within King Street. If so we want to hear from them.
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“We would also like to remind people that it is always a good idea to stick with friends when on a night out, and that includes sharing pre-arranged transportation home.”
Anyone with information can telephone DI Brown, in confidence, on 101 or Crimestoppers, anonymously on 0800 555 111.