  Axion dark matter differentiates the phase velocities of the
circular-polarized photons. In this Letter, a scheme to measure the phase
difference by using a linear optical cavity is proposed. If the scheme is
applied to the Fabry-P\'erot arm of Advanced LIGO-like (Cosmic-Explorer-like)
gravitational wave detector, the potential sensitivity to the axion-photon
coupling constant, $g_{\text{a}\gamma}$, reaches $g_{\text{a}\gamma} \simeq
8\times10^{-13}$ GeV$^{-1}\, (4 \times 10^{-14}$ GeV$^{-1})$ at the axion mass
$m \simeq 3\times 10^{-13}$ eV ($2\times10^{-15}$ eV) and remains at around
this sensitivity for 3 orders of magnitude in mass. Furthermore, its
sensitivity has a sharp peak reaching $g_{\text{a}\gamma} \simeq 10^{-14}$
GeV$^{-1}$ $(8\times10^{-17}$ GeV$^{-1})$ at $m = 1.563\times10^{-10}$ eV
($1.563\times10^{-11}$ eV). This sensitivity can be achieved without loosing
any sensitivity to gravitational waves.
