  The capability of the LHC to study the electromagnetic dipole moments of the
top quark is discussed. In particular, the process $pp\to p\gamma\gamma p\to
pt\bar{t}p$, which is supposed to be tagged by the forward/backward detectors
at the LHC experiments, is used to explore the top quark electric and magnetic
moments. We perform analytical calculations and then a numerical analysis on
the sensitivity of the total cross section of the top quark pair production in
$\gamma\gamma$ scattering at the LHC to the anomalous top quark couplings with
photon. It is shown that improvements in the bounds on the electromagnetic
dipole moments of the top quark can be achieved in this channel in comparison
with the constraints from the former studies.
