The Event Horizon Telescope (EHT) with unprecedented angular resolution opens exciting opportunities to search for new physics beyond the particle Standard Model. Recently, the polarization properties of the radiation near the supermassive black hole M87$^star$ are measured in four individual days. This is exactly what is needed to test the existence of a dense axion cloud produced from extracting the black hole spinning energy by the superradiance mechanism. The presence of the axion cloud leads to a frequency independent oscillation to the electric vector position angle (EVPA) of the linearly polarized radiation. For M87$^star$, which is approximately face-on, such an oscillation of the EVPA appears as a propagating wave along the azimuthal angle on the sky. In this paper, we apply the azimuthal distribution of EVPA measured by the EHT and study the axion-photon coupling. We propose a novel differential analysis procedure to minimize the astrophysical background and derive stringent constraints on the axion parameters. The EHT data can rule out a considerable portion of the axion parameter space for axion mass window $sim (10^{-21}-10^{-20})$~eV, which was unexplored by previous experiments.
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