A stepper motor moves with steps which are normally fed into a control circuitry that takes care of controlling the actual stepper motor
Controlling a stepper motor with the serial port alone could be possibly done by using the control lines as discretes and feeding them into the control circuitry of the stepper. But I would not recommend this at all, since you are most likely to lose steps, etc.
The best way would be to have a microprocessor hooked up to your PC and you send commands vis the serial port such that the microprocessor is able to translate that to the control lines for the stepper control circuitry.
Regards,
Ivancho