The triple gauge couplings are completely defined by the non-Abelian gauge nature of the Standard Model, precision measurements of these couplings at the present and future colliders in this way provide a substantial opportunity to test the gauge structure of the Standard Model. Also, measurements of these couplings are sensitive to new physics beyond the Standard Model. In this context, these couplings can be described by an effective Lagrangian. Here, we have studied the potential of the future mu p colliders on the anomalous WW. interactions via the subprocess gamma* p -> W- nu(mu). This subprocess has been generated through the main process mu(p) -> mu gamma* p -> W-nu(mu)p at the LHC-mu p, the FCC-mu p and the SPPC-mu p. For these reasons, the total cross sections have been obtained as a function of the anomalous WW gamma couplings. Also, we have been calculated the best constraints on cWWW, cW and cB parameters that define the anomalous WW gamma interactions.