  The complete QED corrections of O(alpha) to polarized Compton scattering are
calculated for finite electron mass and including the real corrections induced
by the processes e^- gamma -> e^- gamma gamma and e^- gamma -> e^- e^- e^+. All
relevant formulas are listed in a form that is well suited for a direct
implementation in computer codes. We present a detailed numerical discussion of
the O(alpha)-corrected cross section and the left-right asymmetry in the energy
range of present and future Compton polarimeters, which are used to determine
the beam polarization of high-energetic e^+- beams. For photons with energies
of a few eV and electrons with SLC energies or smaller, the corrections are of
the order of a few per mille. In the energy range of future e^+e^- colliders,
however, they reach 1-2% and cannot be neglected in a precision polarization
measurement.
