Mechanical systems can be influenced by a wide variety of small forces, ranging from gravitational to optical, electrical, and magnetic. When mechanical resonators are scaled down to nanometer-scale dimensions, these forces can be harnessed to enable coupling to individual quantum systems. We demonstrate that the coherent evolution of a single electronic spin associated with a nitrogen vacancy center in diamond can be coupled to the motion of a magnetized mechanical resonator. Coherent manipulation of the spin is used to sense driven and Brownian motion of the resonator under ambient conditions with a precision below 6 picometers. With future improvements, this technique could be used to detect mechanical zero-point fluctuations, realize strong spin-phonon coupling at a single quantum level, and implement quantum spin transducers.