Aims. We present the obliquity measurement, that is, the angle between the normal angle of the orbital plane and the stellar spin axis, of the sub-Neptune planet HD 3167 c, which transits a bright nearby K0 star. We study the orbital architecture of this multi-planet system to understand its dynamical history. We also place constraints on the obliquity of planet d based on the geometry of the planetary system and the dynamical study of the system. Methods. New observations obtained with HARPS-N at the Telescopio Nazionale Galileo (TNG) were employed for our analysis. The sky-projected obliquity was measured using three different methods: the Rossiter-McLaughlin anomaly, Doppler tomography, and reloaded Rossiter-McLaughlin techniques. We performed the stability analysis of the system and investigated the dynamical interactions between the planets and the star. Results. HD 3167 c is found to be nearly polar with sky-projected obliquity, λ = −97 • ± 23 •. This misalignment of the orbit of planet c with the spin axis of the host star is detected with 97% confidence. The analysis of the dynamics of this system yields coplanar orbits of planets c and d. It also shows that it is unlikely that the currently observed system can generate this high obliquity for planets c and d by itself. However, the polar orbits of planets c and d could be explained by the presence of an outer companion in the system. Follow-up observations of the system are required to confirm such a long-period companion.