We study the anomalous W W γ couplings at the Compact Linear Collider through the processes e + e is the Weizsacker-Williams photon). We give the 95% confidence level limits for unpolarized and polarized electron (positron) beam on the anomalous couplings for various values of the integrated luminosities and center-of-mass energies. We show that the obtained limits on the anomalous couplings through these processes can highly improve the current experimental limits. In addition, our limits with beam polarization are approximately two times better than the unpolarized case.Hereκ, λ are the dimensionless anomalous parameters. They are related to magnetic dipole and electric quadrupole moments of W boson. In the SM, the couplings are obtained g γ 1 = 1, κ = 1 and λ = 0 at the tree level. The g γ 1 = 1 value is fixed for on-shell photons at tree level by electromagnetic gauge invariance to its SM value. Then, the Feynman rule for the anomalous vertex can be found from Eq.(1),