Cosmic Microwave Background (CMB) photons can undergo resonant conversion into axions in
the presence of magnetized plasma distributed inside non-linear large-scale structure (LSS). This
process leads to axion-induced patchy screening: secondary temperature and polarization
anisotropies with a characteristic non-blackbody frequency dependence that are strongly
correlated with the distribution of LSS along our past light cone. We compute the axion-induced
patchy screening contribution to two- and three- point correlation functions that include CMB
anisotropies and tracers of LSS within the halo model. We use these results to forecast the
sensitivity of existing and future surveys to photon-axion couplings for axion masses between
2 × 10-13 eV and 3 × 10-12 eV, using a combination of empirical estimates from
Planck data of the contribution from instrumental noise and foregrounds as well as modeled
contributions on angular scales only accessible with future datasets. We demonstrate that an
analysis using Planck and the unWISE galaxy catalogue would be complementary to the most sensitive
existing astrophysical axion searches, probing couplings as small as 3 × 10-12
GeV-1, while observations from a future survey such as CMB-S4 could extend this reach by
almost an additional order of magnitude.