Coherent spin oscillations were nonthermally induced by circularly polarized pulses in the fully compensated antiferromagnet NiO. This effect is attributed to the action of the effective magnetic field generated by an inverse Faraday effect on the spins. The novelty of this mechanism is that spin oscillations are driven by the time derivative of the effective magnetic field which acts even on "pure'' antiferromagnets with zero net magnetic moment in the ground state. The measured frequencies (1.07 THz and 140 GHz) correspond to the out-of-plane and in-plane modes of antiferromagnetic spin oscillations.