The measurement of the top-quark anomalous electromagnetic couplings is one of the most important goals of the top-quark physics program in the present and future collider experiments. This would provide direct information on the non-standard interactions of the top quark. We study a top-quark pair production scenario at the Future Circular Hadron-Electron Collider (FCC-he) through $e^-p \to e^-\gamma p \to \bar t \nu_e b p$ collisions, which will provide information about sensitivities on anomalous $\hat{a}_V$ and $\hat{a}_A$ couplings at a 95\% C.L., and the possibility of probing new physics.