The axion, as a leading dark matter candidate, is the target of many ongoing and proposed experimental searches based on its coupling to photons. Ultralight axions that couple to photons can also cause polarization rotation of light which can be probed by the cosmic microwave background. In this work, we show that a large axion field is inevitably developed around black holes due to the Bose-Einstein condensation of axions, enhancing the induced birefringence effects. Therefore, measuring the modulation of supermassive black hole imaging polarization angles is a strong probe to the axion-photon coupling due to the formation of the axion condensation (axion star) which enhances the axion field. The oscillating axion field around black holes induces polarization rotation on the black hole image, which is detectable and distinguishable from astrophysical effects on the polarization angle, as it exhibits distinctive temporal variability and frequency invariability. In this work, we perform the theoretical calculation on the axion star formation rate and correspondingly the enhanced axion field value near supermassive black holes. Then, we present the range of axion-photon couplings within the axion mass range $10^{−21}–10^{−16}  eV$ that can be probed by the Event Horizon Telescope. The axion parameter space probed by black hole polarimetry will expand with the improvement in sensitivity on the polarization measurement and more black hole polarimetry targets with determined black hole masses.