Take the continuous power rating of your inverter, divide by the AC output voltage and multiply the result by 1.25.

For example, the OutBack Power VFXR3648A-01 inverter has a continuous power rating of 3600 watts, divided by the AC output voltage of 120VAC equals 30. Multiply 30 x 1.25 to arrive at 37.5. Round up to the next available size breaker and you have a 40 amp breaker.

(3600 Watts / 120 VAC) x 1.25 = 37.5

A breaker that may work in this application is the MidNite Solar MNEAC40 Circuit Breaker 40A 120V.