We have examined the anomalous electromagnetic moments of the tau lepton in the processes e(-)gamma -> nu(e)tau(nu) over bar tau (gamma is the Compton backscattering photon) and e(-)e(+)-> e(-)gamma*e(+) -> e(-)gamma -> nu(e)tau(nu) over bar tau (gamma* is the Weizsacker-Williams photon) with unpolarized and polarized electron beams at the CLIC. We have obtained 95% confidence level bounds on the anomalous magnetic and electric dipole moments for various values of the integrated luminosity and center-of-mass energy. Improved constraints of the anomalous magnetic and electric dipole moments have been obtained compared to the LEP sensitivity. (C) 2017 The Authors. Published by Elsevier B.V.