A joule thief circuit takes a low voltage and low current from an almost dead battery cell and boosts the voltage high enough in pulses to dimly light an LED. Since power= voltage times current then by boosting the voltage then the output current is less than the weak battery current.
The output from a joule thief is DC pulses, not AC.
An electric motor needs a certain voltage and uses a certain amount of current but you did not say them. The current used by the motor is probably much too high for a joule thief circuit, use a battery with a high enough voltage and enough current capacity to power the motor for as long as you want.
You can make a different, much more powerful circuit to boost voltage to drive your motor, but you need to know the voltage and current specifications of the motor.