The black BMW Z3 car was seen weaving in and out of traffic in Worcester, potentially endangering lives, a West Mercia Police spokesman said.
The car was taken from St Mary's Street on Thursday evening and was driven down City Walls Road, narrowly missing several vehicles.
Police urged anyone who saw the car to contact them.
A spokesman said: "Because of the way the car was being driven it will have been noticed by a considerable number of people - some of whom may have had their lives put in danger.
"We would like to hear from anyone who saw the car, not only so that we can identify the driver and track the vehicle, but also to find witnesses to what may be careless or dangerous driving."
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