That relay is rated for 5 Amps, which at 12 Volts means it can switch a 60 Watt load (12 x 5) with zero margin. I'm guessing your TV needs more than 60 Watts, but you can check on the nameplate. It may even say how much current it needs. Fortune favors those who operate with safety margins.
So probably not, but a similar relay with a higher current rating would be a good candidate.
Connecting a relay to a digital output pin requires a transistor, a base resistor for the transistor, and a flyback diode. If you search the forum there are plenty of examples.
-br