A high finesse optical cavity can be used to search for cosmic axions in the mass range 10;{-6} < m_{a} < 10;{-4} eV. Either a two-arm or a single-arm cavity is suitable, and in either case the signal appears as resonant sidebands imposed on the carrier. Assuming for the local axion density the usual figure of rho_{a} = 500 Mev/cm;{3}, the KSVZ axion line g_{agammagamma}/m_{a} = 0.4 GeV-2, can be reached over the full mass range in a 1 yr search.