Control 220V stepper motor with arduino?
While a stepper motor is a synchronous motor, the motor you have is meant to be driven by 50/60 Hz @240 volts.

The datasheet clearly shows how to drive it from a relay:



You could do this from an Arduino with the correct rating relay. 

However the motor is not going to operate in a stepping mode where you can control the number of steps using a relay circuit.