In this study, we investigate the potential of the process pp -> p gamma*p -> p tau(nu) over bar (tau)q' 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 alpha(tau) and vertical bar d(tau)vertical bar 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. (C) 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).