We demonstrate an all-optical magnetometer capable of measuring the magnitude and direction of a magnetic field using nonlinear magneto-optical rotation in cesium vapor. Vector capability is added by effective modulation of the field along orthogonal axes and subsequent demodulation of the magnetic-resonance frequency. This modulation is provided by the ac Stark shift induced by circularly polarized laser beams. The sensor exhibits a demonstrated rms noise floor of ∼65 fT/√[Hz] in measurement of the field magnitude and 0.5 mrad/√[Hz] in the field direction; elimination of technical noise would improve these sensitivities to 12 fT/√[Hz] and 10 μrad/√[Hz], respectively. Applications for this all-optical vector magnetometer would include magnetically sensitive fundamental physics experiments, such as the search for a permanent electric dipole moment of the neutron.