We propose a scheme to efficiently tune the scattering length of two colliding ground-state atoms by offresonantly coupling the scattering state to an excited Rydberg molecular state using laser light. For the s-wave scattering of two colliding 87Rb atoms, we demonstrate that the effective optical length and pole strength of this Rydberg optical Feshbach resonance can be tuned over several orders of magnitude, while incoherent processes and losses are minimized. Given the ubiquity of Rydberg molecular states, this technique should be generally applicable to homonuclear atomic pairs as well as to atomic mixtures with s-wave (or even p-wave) scattering.