  Axions and axion-like particles (ALPs) are some of the best-motivated dark
matter (DM) candidates. Under certain circumstances, large axion fluctuations
in the early universe can collapse to form dense configurations called axion
clumps. The densest axion clumps are metastable states known as oscillons. In
this paper we propose a new class of observables that exploit the axion's
coupling to photons. As a result of this coupling an axion clump acts like an
inhomogeneous refractive optical medium -- a lens -- that causes anomalous
dispersion of incident electromagnetic waves. The dispersion of electromagnetic
waves by axion clumps clearly distinguishes this lensing effect from
gravitational lensing. Axion clumps passing in front of background radio
sources act as lenses and lead to apparent positional shifts that can
potentially be discovered by high-precision radio astrometry missions with the
forthcoming Square Kilometer Array (SKA). We discuss the sensitivity of SKA to
lensing effects in a variety of axion halo models. While gravitational
microlensing surveys have placed strong constraints on the amount of DM that
exists in the form of non-luminous astrophysical objects they have been unable
to do so for objects in the mass range $[10^{-14}, 10^{-11}] M_\odot$. We find
that, over a wide range of parameter space, SKA will be sensitive to optical
lensing by oscillons in the mass range that is currently unconstrained by
microlensing surveys.
