The pursuit of discovery in particle physics has always required study at the highest possible energies. Multi-TeV muon colliders, which have important advantages, offer unprecedented potential for investigating new physics beyond the Standard Model. We extensively assume a range of center-of-mass energies from 3 to 100 TeV and a range of integrated luminosities from 1 to 1000 ab −1 for future multi-TeV muon colliders. We perform a phenomenological study of the anomalous W W γ couplings via the process µ + µ − → µ + γ * µ − → µ + W − ν µ using a model-independent analysis in the effective field theory framework at multi-TeV muon colliders. All signal events in the existence of anomalous c W W W /Λ 2 , c W /Λ 2 and c B /Λ 2 couplings and the relevant background events are calculated in MadGraph. The sensitivity estimates obtained for the anomalous W W γ couplings at systematic uncertainties of δ sys = 0, 3, 5% are compared with the experimental results.Our best sensitivity limits at 95% confidence level for c W W W /Λ 2 , c W /Λ 2 and c B /Λ 2 couplings are [−0.0000329; 0.0000241] TeV −2 , [−0.025594; 0.029431] TeV −2 and [−0.025634; 0.029427] TeV −2 at the multi-TeV muon collider with center-of-mass energy of 100 TeV and integrated luminosity of 1000 ab −1 , respectively.