The pursuit of discovery in particle physics has always required study at the highest possible energies. Multi-TeV muon col-liders, 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 WW & gamma; couplings via the process & mu;+& mu;- & RARR; & mu;+& gamma; *& mu;- & RARR; & mu;+-& nu;& nu; over bar  using a model-independent analysis in the effective field theory framework at multi-TeV muon colliders. The sensitivity estimates obtained for the anomalous WW & gamma; couplings at systematic uncertain-ties of & delta;sys = 0%, 3%, 5% are compared with the experimental results. Our best sensitivity limits at 95% confidence level for cWWW/2, c & SIM;WWW/2, cB/2, cW/2, and cW & SIM; /2 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.