What size breaker should be used for a 3.6 kW oven?

3000 / 240 = Amps. You de-rate a breaker by 20 % for continuous load like an oven. You could get by with a 20 Amp breaker and 12 AWG wire. However, I would recommend 30 Amps and 10 AWG for an oven for the long run.