We have investigated the constraints on the anomalous $tq\gamma$ and $tqH$ $(q=u,c)$ couplings through the photoproduction processes $pp\to p\gamma p\to pt\gamma X\to pb{l}^{+}{\nu }_l\gamma X$ and $pp\to p\gamma p\to ptHX\to pb{l}^{+}{\nu }_{l}b\stackrel{-}{b}X$ at the LHC. We have obtained 95% confidence level bounds on the anomalous couplings by considering various values of detector acceptances and integrated luminosities. Improved constraints on the $tq\gamma$ coupling have been obtained compared to current bounds.