The present study explores a novel approach to establish a new bound on the Lorentz violation parameter $c_{\mu \nu }$ in the muon sector. It is achieved by analyzing the scattering cross-section of electron-positron into muon-antimuon under the influence of a strong magnetic field while considering the anomalous magnetic moment. By the standard model extension, the detected discrepancy between the theoretical and experimental values of the anomalous magnetic moment can be attributed to Lorentz violation. New bounds on the Lorenz-violating coefficients $c_{\mu \nu }$ can be obtained by analyzing the theoretical scattering cross section's magnitude at a specific energy for both theoretical and experimental muon anomalous magnetic momentum values. The recently established bounds for the muon is around $c_{\mathrm{TT}}+0.029c_{\mathrm{XX}}+0.07c_{\mathrm{YY}}+0.039c_{\mathrm{ZZ}}<5.76\times {10}^{-7}$.