  We find an exact, rotating charged black hole solution within
Eddington-inspired Born-Infeld gravity. To this end we employ a recently
developed correspondence or {\it mapping} between modified gravity models built
as scalars out of contractions of the metric with the Ricci tensor, and
formulated in metric-affine spaces (Ricci-Based Gravity theories) and General
Relativity. This way, starting from the Kerr-Newman solution, we show that this
mapping bring us the axisymmetric solutions of Eddington-inspired Born-Infeld
gravity coupled to a certain model of non-linear electrodynamics. We discuss
the most relevant physical features of the solutions obtained this way, both in
the spherically symmetric limit and in the fully rotating regime. Moreover, we
further elaborate on the potential impact of this important technical progress
for bringing closer the predictions of modified gravity with the astrophysical
observations of compact objects and gravitational wave astronomy.
