  CP-violating asymmetries due to a possible electric dipole interaction of the
top quark in the production and subsequent decay of top quark-top antiquark
pair in photon-photon collisions are studied. The asymmetries defined can be
used to determine the imaginary part of the electric dipole form factors. A
gamma-gamma collider with photon beams generated from laser back-scattering off
electron beams with an integrated geometric luminosity of 20 fb^{-1} can put a
limit of the order of 10^{-17} e cm on the imaginary part of the electric
dipole form factor of the top quark if the electron beams have longitudinal
polarization and the laser beams have circular polarization.
