Not officially, except for evenings and Sundays in most council-managed car parks. There is some free parking for motorbikes and, subject to some restrictions, for disabled badge holders, but officially you have to pay for on-street parking and, in practice, most roads near the centre have meters or double yellow lines. As with most cities, it's probably better to go straight to a car park than to spend a lot of time trying to find a space in a side street. To make things easier you can use the Parking Planner.
For people who regularly drive into the centre, it is often possible to arrange to rent a parking space from a local resident. Schemes like this will probably become more popular in future, as Norwich council is about to put up its car park charges.