On Dec. 17, Officer Gregory Hui was suspended from duty without pay while the internal affairs division and the criminal investigations unit looked into the incident, police said.
A warrant was issued for his arrest following the investigation, but police declined to disclose the date it was dealt.
He was booked into San Francisco County Jail and is being held on two felony charges of fraudulent use of vehicle registration and on a misdemeanor charge of theft while in uniform, Officer Eric Chiang said.
Hui had been been working for the police department for about eight years prior to his arrest, he said.
Chiang declined to provide further information about the case.