  In this study, we investigate the potential of the process $pp\rightarrow
p\gamma^{*} p\rightarrow p \tau \bar{\nu}_{\tau}q^{\prime} X$ at the LHC to
examine the anomalous electromagnetic moments of the tau lepton. We obtain
$95\%$ confidence level bounds on the anomalous coupling parameters with
various values of the integrated luminosity and center-of-mass energy. The
improved bounds have been obtained on the anomalous coupling parameters of
electric and magnetic moments of the tau lepton $a_{\tau}$ and
$\vert$$d_{\tau}$$\vert$ compared to the current experimental sensitivity
bounds. The $\gamma p$ mode of photon reactions at the LHC have shown that it
has great potential for the electromagnetic dipole moments studies of the tau
lepton.
