  The general relativistic effects to the anomalous magnetic moment of muons
moving in the Earth's gravitational field have been examined. The Dirac
equation generalized to include the general relativity suggests the magnetic
moment of fermions measured on the ground level is influenced by the Earth's
gravitational field as $\mu_{\rm m}^{\rm eff} \!\simeq\!
(1\!+\!3\phi/c^2)\,\mu_{\rm m}$, where $\mu_{\rm m}$ is the magnetic moment in
the flat spacetime and $\phi\!=\!-{G M}/{r}$ is the Earth's gravitational
potential. It implies that the muon anomalous magnetic moment measured on the
Earth $a_\mu\!\equiv\!{\rm g}_\mu/2\!-\!1$ contains the gravitational
correction of $\left\vert a_\mu\right\vert\simeq 2.1\!\times\! 10^{-9}$ in
addition to the quantum radiative corrections. The gravitationally induced
anomaly may affect the comparison between the theoretical and experimental
values recently reported: $a_{\mu({\rm EXP})}-a_{\mu({\rm
SM})}=28.8\,\,(8.0)\times10^{-10}\,\,(3.6\,\sigma)$. In this paper, the
comparison between the theory and the experiment is examined by considering the
influence of the spacetime curvature to the measurement on the muon ${\rm
g}_\mu\!\!-\!2$ experiment using the storage ring on the basis of the general
relativity up to the post-Newtonian order of $O(1/c^2)$.
