In a photoionization experiment involving polarized alkali atoms and circularly polarized photons we measured the strength of the spin-orbit perturbation in potassium, rubidium, and cesium. Our results are pertinent to the theory of photoionization and to the production of polarized electrons. Extrapolation of the results to photon energies below the ionization threshold provides access to the anomalous doublet line-strength ratio of discrete P states.