Expressions are developed for the flux and polarization of radiation scattered by a spherically symmetric envelope for a central point stellar light source that radiates anisotropically. These are obtained in terms of the components of the spherical harmonics of the flux anisotropy from the source. Such anisotropy can arise from stellar spots, or from distortion of the star through rotation, pulsation, or magnetic effects. Explicit expressions for the Stokes parameters are obtained in the case of an ellipsoidal star of uniform surface brightness. It is thus shown that even when the scattering envelope is spherical, observationally significant polarization can arise from stars with physically realistic degrees of distortion. The time dependence of the polarization is computed for models of ellipsoidal stars in the cases of pure rotation, pure pulsation, and both rotation and pulsation.