We propose a gyroscopic effect based on the geometric phase that can arise in Rydberg atoms, similar to the non-Abelian quantum mechanical geometric phase, enabling the use of Rydberg states for measuring mechanical rotation. Here we take advantage of the super-integrability of the Kepler problem, which gives rise to geometric phase effects resembling the rotation of the Foucault pendulum, but occurring on sub-millisecond time scales.