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 30 TeV and a range of integrated luminosities from 1 to 90 ab−1 for future multi-TeV muon colliders. We perform a phenomenological study of the anomalous WWγ couplings via the process [Formula: see text] using a model-independent analysis in the effective field theory framework at multi-TeV muon colliders. The sensitivity estimates obtained for the anomalous WWγ couplings at systematic uncertainties of δsys = 0%, 3%, 5% are compared with the experimental results. Our best sensitivity limits at 95% confidence level for cWWW/Λ2, [Formula: see text], c B /Λ2, c W /Λ2, and [Formula: see text] couplings are [−0.030; 0.025], [−0.014; 0.014], [−0.185; 0.187], [−0.187; 0.189], and [−1.177; 1.097] TeV−2 at the multi-TeV muon collider with center-of-mass energy of 30 TeV and integrated luminosity of 90 ab−1, respectively.