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.
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