Starting from an effective Lagrangian for the [Formula: see text] interaction of the top-quark, we consider the electroweak production cross-section via charged current and through the [Formula: see text] signal. Further, we derive the sensitivity expected for the magnetic dipole moment [Formula: see text] and the electric dipole moment [Formula: see text] of the top-quark at the Future Circular Collider-hadron electron (FCC-he). We present our study for [Formula: see text], 10 TeV, [Formula: see text], 100, 300, 500, 1000 fb[Formula: see text], [Formula: see text] and [Formula: see text], 80%, [Formula: see text], respectively. We find that the sensitivity estimated on dipole moments of the top-quark is of the order of magnitude [Formula: see text] for both hadronic and leptonic decay modes of [Formula: see text]: [Formula: see text] and [Formula: see text] at 95% C.L. in the hadronic channel with unpolarized electron beam [Formula: see text]. Our results regarding the polarized electron beam for [Formula: see text] and [Formula: see text] are [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text] at 95% C.L. in the hadronic channel. The corresponding results for the leptonic channel with [Formula: see text], 80% [Formula: see text] are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], respectively. The results for [Formula: see text] and [Formula: see text] in the leptonic channel are weaker than those corresponding to the hadronic channel by a factor of 0.75. Given these prospective sensitivities, the FCC-he is an alternative to study the anomalous couplings of the quark-top that would complement the studies of the LHC with cleaner environments.