The resonant conversion of cosmic microwave background (CMB) photons into axions within large-scale structure induces an anisotropic spectral distortion in CMB temperature maps. Applying state-of-the-art foreground cleaning techniques to Planck CMB observations, we construct maps of axion-induced "patchy screening" of the CMB. We cross-correlate these maps with data from the unWISE galaxy survey and find no evidence of axions. We constrain the axion-photon coupling, g_{aγγ}≲2×10^{-12} GeV^{-1}, at the 95% confidence level for axion masses in the range 10^{-13} eV≲m_{a}≲10^{-12} eV. These constraints are competitive with the tightest astrophysical axion limits in this mass range and are inferred from robust population-level statistics, which makes them complementary to existing searches that rely on modeling of individual systems.