We calculate the effects of frame dragging on the Galactic-Center stars. Assuming the stars are only slightly relativistic, we derive an approximation to the Kerr metric, which turns out to be a weak-field Schwarzschild metric plus a frame-dragging term. By numerically integrating the resulting geodesic equations, we compute the effect on Keplerian elements and the kinematics. We find that the kinematic effect at pericenter passage is proportional to (a(1 – e 2))–2. For known Galactic-center stars it is of order 10 m s–1. If observed, this would provide a measurement of the spin of the black hole.