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Observation of top quark flavor changing neutral process $t\to c +\gamma$ atthe LHC would be the signal of physics beyond the Standard Model. If anomalous$t\to c\gamma$ coupling exists, it will affect the precisely measured$\mathcal{B}(\bar{B} \to X_s \gamma)$. In this paper, we study the effects of adimension 5 anomalous $ tc \gamma$ operator in $\bar{B} \to X_s \gamma$ decayto derive constraints on its possible strength. It is found that, for realanomalous $t\to c\gamma$ coupling $\kappa_{\rm{tcR}}^\gamma$, the constraintscorrespond to the upper bounds $\mathcal B (t \to c + \gamma)<6.54 \times10^{-5}$ (for $\kappa_{\rm{tcR}}^\gamma>0$) and $\mathcal B (t \to c +\gamma)<8.52 \times 10^{-5}$ (for $\kappa_{\rm{tcR}}^\gamma<0$), respectively,which are about the same order as the $5\sigma$ discovery potential of ATLAS($9.4\times 10^{-5}$) and slightly lower than that of CMS ($4.1\times 10^{-4}$)with $10 \ \rm{fb}^{-1}$ integrated luminosity operating at $\sqrt{s} =14$ TeV.

B -> Xs\gamma constraints on the top quark anomalous t-> c\gamma coupling