Radiative corrections to the muon polarization vector in $K_{\mu 3}^{\pm }$ decays have been calculated. The model, previously used, is based on a phenomenological weak $K-\pi$ vertex and perturbation theory. The answer depends logarithmically on a cutoff, although the corrections are not nearly as sensitive to variations in the cutoff as those for unpolarized decays. All terms which contribute to order $\alpha$ have been retained, with no approximations concerning the smallness of the muon mass or the "real" inner bremsstrahlung. The corrections to the three components of the polarization vector (longitudinal, transverse, and perpendicular) have been evaluated numerically at points in the Dalitz plot, for various complex values of $\xi$. In addition, the integrated correction to the degree of polarization as a function of muon energy has also been computed. It is found that these corrections are small, generally less than or equal to 1%, except in kinematically queer regions, where their relative size can be appreciable.

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