The Gravitational Wave (GW) event GW 170817 was generated by the coalescence of two neutron stars (NS) and produced an electromagnetic transient, labelled AT 2017gfo, that was target of a massive observational campaign. Polarimetry, a powerful diagnostic tool for probing the geometry and emission processes of unresolved sources, was obtained for this event. The observed linear polarization was consistent with being mostly induced by intervening dust, suggesting that the intrinsic emission was weakly polarized ($P < 0.4-0.5$ %). In this paper, we present and discuss a detailed analysis of the linear polarization expected from a merging NS binary system by means of 3D Monte Carlo radiative transfer simulations assuming a range of possible configurations, wavelengths, epochs and viewing angles. We find that polarization originates from the non-homogeneous opacity distribution within the ejecta and can reach levels of $Psim1$ % at early times (1$-$2 days after the merger) and in the optical R band. Smaller polarization signals are expected at later epochs and/or different wavelengths. From the viewing-angle dependence of the polarimetric signal, we constrain the observer orientation of AT 2017gfo within $sim$65$^circ$ from the polar direction. The detection of non-zero polarization in future events will unambiguously reveal the presence of a lanthanide-free ejecta component and unveil its spatial and angular distribution.
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