In a large range of physics and space experiments, the direction of the magnetic field needs to be determined with an accuracy on the level of one milli radian or better. We have proposed a new type of magnetic compass - a rotation-based one, which provides an alternating signal from the Hall probe proportional to the value of the magnetic field transverse to the axis of rotation. The spinning Hall probe device has been realized. Alignment of the spinning axis for a minimum (zero) value of the signal allows us to find the direction of the magnetic field. The device does not require calibration and is free of any drift problems. The measurement of the rotation axis direction was accomplished by means of a laser and a flat mirror attached to the rotor. The constructed prototype achieved an accuracy for the magnetic field direction in the experiment with the polarized He-3 target on the level of one milli radian.