  We realize a phenomenological study to examine the sensitivity on the
magnetic moment and electric dipole moment of the top quark through the
processes $\gamma\gamma\rightarrow t \bar{t}$, $e \gamma \rightarrow e
\gamma^{*} \gamma \rightarrow e t \bar{t}$ and $e^{-} e^{+}\rightarrow e^{-}
\gamma^{*} \gamma^{*} e^{+} \rightarrow e^{-} t \bar{t}e^{+}$ at the CLIC. We
find that with a center-of-mass energy of the CLIC-1.4$\hspace{0.8mm}TeV$,
integrated luminosity of ${\cal L}=1500\hspace{0.8mm}fb^{-1}$ and
CLIC-3$\hspace{1mm}TeV$, integrated luminosity of ${\cal
L}=2000\hspace{0.8mm}fb^{-1}$ with systematic uncertainties of $\delta_{sys}=0,
5, 10\hspace{1mm}\%$ at the $95\%\hspace{1mm}C. L.$, it is possible the CLIC
may put limits on the electromagnetic dipole moments of the top quark $\hat
a_V$ and $\hat a_A$ with a sensitivity of ${\cal O}(10^{-3}-10^{-2})$.
Therefore, we show that the sensitivity with the CLIC data is much greater than
that for the LHC data.
