The man was arrested at his grandparents house on Sunday on charges of theft, causing injury and sexual assault, and taken to Regina Coeli prison, La Repubblica reported.
He allegedly raped the woman early on Friday, after telling her to drive to Ponte Galeria in the outskirts of Rome.
He reportedly told police that he had been overcome by “a burst of rage, a mad impulse in the moment”.
He is also said to have a history of petty theft and not paying taxis.
Meanwhile, there is mounting protest among the capital's taxi drivers, who are calling for better security and protection against abuse. They also plan to strike, La Repubblica said.