  We consider the density profile of pressureless dark matter in
Eddington-inspired Born-Infeld (EiBI) gravity. The gravitational field
equations are investigated for a spherically symmetric dark matter galactic
halo, by adopting a phenomenological tangential velocity profile for test
particles moving in stable circular orbits around the galactic center. The
density profile and the mass distribution, as well as the general form of the
metric tensor is obtained by numerically integrating the gravitational field
equations, and in an approximate analytical form by using the Newtonian limit
of the theory. In the weak field limit the dark matter density distribution is
described by the Lane-Emden equation with polytropic index $n=1$, and is
non-singular at the galactic center. The parameter $\kappa $ of the theory is
determined so that that the theory could provide a realistic description of the
dark matter halos. The gravitational properties of the dark matter halos are
also briefly discussed in the Newtonian approximation.
