We consider the branching ratio for the process $t o c gamma$ in the context of the General Two Higgs Doublet Model type III. We find that taking into account reasonable values for the parameter $ an eta$ is possible to get values of this branching ratio up to orders of magnitude lying in the range of sensitivity of near future top quark experiments. For values of $B(t o c gamma) sim 1-9 imes 10^{-5}$, values between 8-15 for $ an eta$ are allowed.