The cross section for gamma gamma --> W+W- with arbitrary polarized ph
otons 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 correction
s, It turns our that in the on-shell renormalization scheme for fixed
M(w) no leading corrections associated with the running of alpha or he
avy top-quark and Higgs-boson masses occur. The corrections are typica
lly of the order of 10%. They reach, however, larger values where the
lowest-order cross sections are suppressed.