A search for charged-lepton-flavor violating μτqt (q=u, c) interactions is presented, considering both top-quark production and decay. The data analyzed correspond to 140 fb−1 of proton-proton collisions at a center-of-mass energy of s=13 TeV recorded with the ATLAS detector at the Large Hadron Collider. The analysis targets events containing two muons with the same electric charge, a hadronically decaying τ-lepton and at least one jet, with exactly one b-tagged jet, produced by a μτqt interaction. Agreement with the Standard Model expectation within 1.6 standard deviations is observed, and limits are set at the 95% confidence level (CL) on the charged-lepton-flavor violation branching ratio of B(t→μτq)