Off hand, you might want to look at stepper motors (http://www.solarbotics.net/library/pieces/parts_mech_steppers.html).
Another possibility is servo motors (Make: Projects). Normally servo motors will only go from 0..180 degrees, but I would expect with a 2:1 gear ratio, you could turn the full 360 degrees in 2 degree increments.
Obviously the selection of motor depends on how fast you need it to go, how much torque you need the motor to move, how much power the motor needs, and what your budget is. Its your project, so get cracking and figure out what parameters you need in a motor.