  We consider the standard model extension to explore the anomalous magnetic
dipole moment of the muon. In the QED part of the theory for the CP and
CPT-even Lorentz parameter $c_{\mu\nu}$, all independent electromagnetic form
factors depend on a new scalar as $p'.c.p$. Therefore, the form factors, even
in zero momentum transfer, can be energy dependent. We examine the magnetic
form factor to find such an energy dependent up to the one loop level at the
leading order of $c_{\mu\nu}$. We show that at the high energy limit (but low
enough to satisfy $p^2/m^2\ll1$) there is an enhancement on the muon anomalous
magnetic moment. For the first time, we find a bound on the $c_{\mu\nu}$
components for the muon as $[c_{TT}+0.35(c_{XX}+c_{YY})+0.28c_{ZZ}]$, which is
about $10^{-11}$ in a terrestrial experiment
