Polarization-dependent excitation of coherent spin precession by 150 fs linearly polarized laser pulses is observed in the easy-plane antiferromagnet FeBO3. We show that the mechanism of excitation is impulsive stimulated Raman scattering. This process is shown to be determined not only by the magneto-optical constants of the material, but also by the properties of the spin precession itself. Though carrying no angular momentum, the linearly polarized laser pulses act on the spins as effective fields that can be considered as an ultrafast inverse Cotton-Mouton effect.