The woman in her 20s reported she was sexually assaulted after getting into the front seat of the taxi at around 2.50am on Saturday, February 10.
It is believed the assault took place near Villiers Street, off Chester Road North.
A man has been arrested on suspicion of sexual assault and released under investigation while enquiries continue.
Detective Constable Marie Holmes said: "This was terrifying incident for the victim and we are keen to speak to anyone who may have information that could help with our enquiries.
"We take all reports of sexual offences extremely seriously and will fully investigate.
"We encourage all victims to call police."
Anyone with information is asked to call West Mercia Police on 101, quoting incident reference number 497S of February 11.
Alternatively, information can be passed on anonymously to the independent charity Crimestoppers on 0800 555111 or by visiting crimestoppers-uk.org.