We have measured the production polarization of 265- and 310-GeV/c Σ− in the inclusive reaction p+Cu→Σ−+X using 400-GeV/c protons. The polarization was analyzed via the asymmetry in the weak decay Σ−→n+π−, and has typical values of +0.20 with respect to the direction of the cross product of the incident-proton and Σ− momenta. Using the spin-precession technique, we have determined the Σ− magnetic moment to be -1.23±0.03±0.03 nuclear magnetons, where the statistical and systematic errors are shown separately.