Anisotropic scintillators can offer a unique possibility to exploit the so-called directionality approach in order to investigate the presence of those Dark Matter (DM) candidates inducing nuclear recoils. In fact, their use can overcome the difficulty of detecting extremely short nuclear recoil traces. In this paper we present recent measurements performed on the anisotropic response of a ZnWO 4 crystal scintillator to nuclear recoils, in the framework of the ADAMO project. The anisotropic features of the ZnWO 4 crystal scintillators were initially measured with α particles; those results have been also confirmed by the additional measurements presented here. The experimental nuclear recoil data were obtained by using a neutron generator at ENEA-CASACCIA and neutron detectors to tag the scattered neutrons; in particular, the quenching factor values for nuclear recoils along different crystallographic axes have been determined for three different neutron scattering angles (i.e. nuclear recoils energies). From these measurements, the anisotropy of the light response for nuclear recoils in the ZnWO 4 crystal scintillator has been determined at 5.4 standard deviations.