Actors will read poems in what organisers said would be "a unique artistic experience".
Members of the public will choose the verses from a list before picking up the cab at an agreed location and time.
Festival artistic director Sarah LeFanu has taken the idea from the Toulouse Festival of Words, in France.
"Bath Literature Festival is a very hands-on festival," she said.
"We like our audiences to debate, discuss, consider and participate and the Poetry Taxi provides a new way for people to do that."
The taxi can be caught over both weekends of the festival: 23 and 24 February and 1 and 2 March.
The theme of the event is Origins and Identities and writers already listed to speak include Steven Berkoff and Terry Pratchett.
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