The cross section for gamma gamma --> W+W- with arbitrary polarized photons and W bosons is calculated within the electroweak Standard Model including the complete virtual and soft-photonic O(alpha) corrections. We present a detailed numerical discussion of the complete radiative corrections and an analytical investigation of the leading corrections, It turns our that in the on-shell renormalization scheme for fixed M(w) no leading corrections associated with the running of alpha or heavy top-quark and Higgs-boson masses occur. The corrections are typically of the order of 10%. They reach, however, larger values where the lowest-order cross sections are suppressed.