  The Electron-Ion Collider~(EIC), a forthcoming powerful high-luminosity
facility, represents an exciting opportunity to explore new physics. In this
article, we study the potential of the EIC to probe the coupling between
axion-like particles~(ALPs) and photons in coherent scattering. The ALPs can be
produced via photon fusion and decay back to two photons inside the EIC
detector. In a prompt-decay search, we find that the EIC can set the most
stringent bound for $m_a \lesssim 20\,\GeV$ and probe the effective scales
$\Lambda \lesssim 10^{5}\,$GeV. In a displaced-vertex search, which requires
adopting an EM calorimeter technology that provides directionality, the EIC
could probe ALPs with $m_a \lesssim 1\,\GeV$ at effective scales $\Lambda
\lesssim 10^{7}\,\GeV$. Combining the two search strategies, the EIC can probe
a significant portion of unexplored parameter space in the $0.2 < m_a
<20\,\GeV$ mass range.
