The top quark flavor changing neutral current processes are extremely suppressed within the Standard Model. Nevertheless, they could be enhanced in a new physics model beyond the Standard Model. Investigating the top quark's flavor changing neutral current interactions at colliders would be an important test in terms of new physics. In this work, we examine the potentials of the processes e(-)p -> e(-)gamma p -> e(-)W(+)b gamma -> e(-)(jj) over barb gamma and e(-)p -> e(-)gamma p -> e-W+b gamma -> e(-)l nu(l)b gamma at the FCC-eh with root s = 7.08 and 10.0 TeV to study anomalous tq gamma couplings via effective Lagrangians. We obtain 95% confidence level sensitivities on the anomalous coupling parameters at the two FCC-eh energies and various integrated luminosities. We find that our limits are at least two orders of magnitude better than the current LHC experimental results.