Norby, 64, was taken into custody Wednesday afternoon and booked at the Fullerton Police Department Jail. He was released a few hours later after posting a $10,000 bond, police said.
His arraignment is scheduled for March 19.
No other details on the arrest were immediately released.
The Republican served as councilman and mayor in Fullerton before joining the Orange County Board of Supervisors. He was elected to the 65th Assembly District seat in a 2010 special election, but was defeated in 2012.
City News Service contributed to this report