It couldn't.

To demonstrate, take a small gyroscope toy and crank it up. That's the revolution of the Earth.

Next, try to rotate it in a direction 90 degrees from that angular momentum. See how much energy it takes to change it. That force would have to come from outside of the earth/moon system to make the scenario work.

That's why a gyroscope, like an angel, can dance on the head of a pin.