  Non-relativistic QCD axions or axion-like particles are among the most
popular candidates for cold Dark Matter (DM) in the universe. We proposed to
detect axion-like DM, using linearly polarized pulsar light as a probe. Because
of birefringence effect potentially caused by an oscillating galactic axion DM
background, when pulsar light travels across the galaxy, its linear
polarization angle may vary with time. With a soliton+NFW galactic DM density
profile, we show that this strategy can potentially probe an axion-photon
coupling as small as $\sim 10^{-13}$ GeV$^{-1}$ for axion mass $m_a \sim
10^{-22}-10^{-20}$ eV, given the current measurement accuracy. An exclusion
limit stronger than CAST ($ \sim 10^{-10}$ GeV$^{-1}$) and SN1987A ($ \sim
10^{-11}$ GeV$^{-1}$) could be extended up to $m_a \sim 10^{-18}$ eV and $\sim
10^{-19}$ eV, respectively.
