The cross section for Gamma Gamma --->T Anti-T with arbitrary polarized photons 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 radiative corrections with particular emphasis on the purely weak corrections. These are usually of the order of 1-10% for energies up to 1 TeV. For unpolarized or equally polarized photons they reach almost 10% close to threshold. The large corrections cannot be traced back to a universal origin such as the running of a or the r parameter. Apart from the energy region around the Higgs resonance (gamma gamma --> H --> tt) the weak corrections are widely independent of the Higgs-boson mass.