This paper is the third in a series on the anisotropic scattering by optically thin resonance lines in extended stellar envelopes. Considered here is the polarization arising from resonance line scattering in equatorial disks. The shape of the polarized line profile is analytically derived under simplifying conditions of constant expansion or rotation for thin lines, with stellar occultation and finite star depolarization effects also included. The polarized profiles for the two cases are radically different. Moreover owing to the symmetries, rotation leads to profiles in both Qν and Uν, whereas only a Qν profile survives for an expanding disk, with Uν=0 at all Doppler shifts in the line. Retaining the assumption of optical thinness, numerical results are presented for more realistic disk velocity fields: truncated linear expansion and Keplerian rotation. The calculations also include disk absorption of stellar continuum emission. When compared with the simplified analytic cases, many of the gross characteristics of the polarized profiles are retained.