The presence of axion strings in the Universe after recombination can leave an imprint on
the polarization pattern of the cosmic microwave background radiation through the phenomenon of
axion-string-induced birefringence via the hyperlight axion-like particle's coupling to
electromagnetism. Across the sky, the polarization rotation angle is expected to display a
patchwork of uniform regions with sharp boundaries that arise as the `shadow' of axion string
loops. The statistics of such a birefringence sky map are therefore necessarily non-Gaussian. In
this article we quantify the non-Gaussianity in axion-string-induced birefringence using two
techniques, kurtosis and bispectrum, which correspond to 4- and 3-point correlation
functions. If anisotropic birefringence were detected in the future, a measurement of its
non-Gaussian properties would facilitate a discrimination across different new physics sources
generally, and in the context of axion strings specifically, it would help to break degeneracies
between the axion-photon coupling and properties of the string network.