  A fraction of light scalar dark matter, especially axions, may organize into
Bose-Einstein condensates, gravitationally bound clumps, "boson stars", and be
present in large number in galactic halos today. We compute the expected number
of gravitational microlensing events of clumps composed of the ordinary QCD
axion and axion-like-particles and derive microlensing constraints from the
EROS-2 survey and the Subaru Hyper Suprime-Cam observation. We perform a
detailed lensing calculation, including the finite lens and source size effects
in our analysis. We constrain the axion mass in terms of the fraction of dark
matter collapsed into clumps, the individual clump densities, and the axion
self-coupling. We also consider and constrain clumps composed of a generic
scalar dark matter candidate with repulsive self-interactions. Our analysis
opens up a new window for the potential discovery of dark matter.
