  We have examined the anomalous electromagnetic moments of the tau lepton in
the processes $e^{-}\gamma \to \nu_e\tau\bar{\nu}_\tau$ ($\gamma$ is the
Compton backscattering photon) and $e^{-}e^{+} \to e^{-}\gamma^* e^{+} \to
\nu_{e}\tau \bar{\nu}_\tau e^+$ ($\gamma^*$ 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.
