  Axions are a viable candidate for Cold Dark Matter (CDM) which should
generically form minihalos of sub-planetary masses from white-noise
isocurvature density fluctuations if the Peccei-Quinn phase transition occurs
after inflation. Despite being denser than the larger halos formed out of
adiabatic fluctuations from inflation, axion minihalos have surface densities
much smaller than the critical value required for gravitational lensing to
produce multiple images or high magnification, and hence are practically
undetectable as lenses in isolation. However, their lensing effect can be
enhanced when superposed near critical curves of other lenses. We propose a
method to detect them through photometric monitoring of recently discovered
caustic transiting stars behind cluster lenses, under extreme magnification
factors $\mu \gtrsim 10^3$--$10^4$ as the lensed stars cross microlensing
caustics induced by intracluster stars. For masses of the first gravitationally
collapsed minihalos in the range $\sim 10^{-15}$--$10^{-8}\,h^{-1}\,M_\odot$,
we show that axion minihalos in galaxy clusters should collectively produce
subtle surface density fluctuations of amplitude $\sim 10^{-4}$--$10^{-3}$ on
projected length scales of $\sim 10$--$10^4\,$AU, which imprint irregularities
in the microlensing light curves of caustic transiting stars. We estimate that,
inside a cluster halo and over the age of the Universe, most of these minihalos
are likely to avoid dynamic disruption by encounters with stars or other
minihalos.
