  We present a calculation of the complete $O(\alpha)$ electroweak radiative
corrections to the Moller scattering process e^-e^- -> e^-e^-, including hard
bremsstrahlung contributions. We study the effects of these corrections on both
the total cross section and polarization asymmetry measured in low energy fixed
target experiments. Numerical results are presented for the experimental cuts
relevant for E-158, a fixed target e^-e^- experiment being performed at SLAC;
the effect of hard bremsstrahlung is to shift the measured polarization
asymmetry by approximately +4%. We briefly discuss the remaining theoretical
uncertainty in the prediction for the low energy Moller scattering polarization
asymmetry.
