The cross section for e(-)e(-) --> e(-)e(-) with arbitrary electron polariz
ations is calculated within the Electroweak Standard Model for energies lar
ge compared to the electron mass, including the complete virtual and soft-p
hotonic O(alpha) radiative corrections. The relevant analytical results are
listed, and a numerical evaluation is presented for the unpolarized and po
larized cross sections as well as for polarization asymmetries. The relativ
e weak corrections are typically of the order of 10%. At low energies, the
bulk of the corrections is due to the running of the electromagnetic coupli
ng constant. For left-handed electrons, at high energies the vertex and box
corrections involving virtual W bosons become very important. The polariza
tion asymmetry is considerably reduced by the weak radiative corrections.