Yes, for a little while.
To do it so the router lasts more than a few days, use a 12v regulator. The 12v of a car isn't really 12v. it can go from 7-14 volts depending on conditions.
If there is room on the 12v rail on the computer power supply (assuming you have one since you want to put a wireless router in a car) you can power it from there too.