In the framework of a collisionless dark matter fluid which is non-minimally coupled to gravity, we investigate the existence and properties of static, spherically symmetric solutions of the general relativistic field equations. We show that the non-minimal coupling originates an (anisotropic) pressure able to counteract gravity and to allow the formation of regular, horizonless ultra-compact objects of dark matter (NMC-UCOs). We then analyze the orbits of massive and massless particles in the gravitational field of NMC-UCOs, providing some specific example and a general discussion in terms of phase portraits. Finally, we study the gravitational lensing effects around NMC-UCOs, and effectively describe these in terms of a pseudo-shadow.
