The normal way to drive a stepper motor is to use switched-dc voltages to energize the stepper motor coils one by one after each other. But a stepper motor will run off ac lines if you introduce a 90° phase shift between the voltages applied to the motor’s two windings. The extremely simple circuit in Fig 1 drives a stepper motor directly from 12V ac , 60 Hz power supply. Four steps equal one ac cycle.
I tested the circuit idea with a slightly different setup and it worked well. I just picked a random small stepper motor I had lying around. It had around 90 ohm coil resistance. I used a 10 uF capacitor (a small electrolytic, dry capacitor would be better for long run). The power source I used was 24V 50Hz AC. The stepper motor run with the circuit nicely at least the short time I tried it. I did not run it for a long time because I did not know the specifications of the stepper motor, and I feared that the 24V AC could be too high for it (could cause overheating on long run).