A simple shift register can do the job. Made from 4 'D' flip-flops.
This shows the bare concept. You may need to finagle with it so it starts up in the correct state. (I say this because the simulation is quirky and needs similar finagling.)
If you want an all-in-one device to do the job, look at the 4017 IC. It's a divide by 10 counter. It can be wired to reset after a lesser number, so that it recycles indefinitely.
I was thinking of a suitable finagle. If you connect three reset inputs and one set input to a common resistor (100 ohms?) to earth. Then pulsing this line high would get your D types in a suitable state. So you now need some thing that delivers a single pulse when the Vcc is applied. Depending on the rise time of the Vcc, a capacitor might do it.
Frank