Yes, you can run a TV off a 12 volt battery. You will need to use an inverter to convert the 12 volt DC power from the battery into 110 volt AC power that is compatible with most TVs. The inverter will also need to be able to provide enough power to run the TV.
Most RV batteries are not powerful enough to run a TV for more than a few minutes, so you may need to use a deep cycle battery or a gel cell battery.