  We investigate the scattering properties of a massless scalar field in the
background of a charged Ay\'on-Beato-Garc\'ia regular black hole solution.
Using a numerical approach, we compute the differential scattering cross
section for arbitrary values of the scattering angle and of the incident wave
frequency. We compare our results with those obtained via the classical
geodesic scattering of massless particles, as well as with the semiclassical
glory approximation, and show that they present an excellent agreement in the
corresponding limits. We also show that Ay\'on-Beato-Garc\'ia and
Reissner-Nordstr\"om black hole solutions present similar scattering
properties, for low-to-moderate values of the black hole electric charge, for
any value of the scattering angle.
