  Today we have quite stringent constraints on possible violations of the Weak
Equivalence Principle from the comparison of the acceleration of test-bodies of
different composition in Earth's gravitational field. In the present paper, we
propose a test of the Weak Equivalence Principle in the strong gravitational
field of black holes. We construct a relativistic reflection model in which
either the massive particles of the gas of the accretion disk or the photons
emitted by the disk may not follow the geodesics of the spacetime. We employ
our model to analyze the reflection features of a NuSTAR spectrum of the black
hole binary EXO 1846-031 and we constrain two parameters that quantify a
possible violation of the Weak Equivalence Principle by massive particles and
X-ray photons, respectively.
