A polarizable potential function describing the interaction between acetonitrile molecules is introduced. The molecules are described as rigid and linear, with three mass sites corresponding to the CH3 group (methyl, Me), the central carbon atom (C), and the nitrogen atom (N). The electrostatic interaction is represented using a single-center multipole expansion as has been done previously for H2O [Wikfeldt et al., Phys. Chem. Chem. Phys. 15, 16542 (2013)], by including multipole moments from dipole up to and including hexadecapole, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model is free of point charges. The non-electrostatic part is described in a pair-wise fashion by a Born-Mayer repulsion and damped dispersion attraction. The potential function is parameterized to fit the interaction energy of small (CH3CN)n, n = 2-6, clusters calculated using the PBE0 hybrid functional with an additional atomic many-body dispersion contribution. The parameterized potential function is found to compare well with results of the electronic structure calculations of dissociation curves for different dimer orientations and cohesive properties (the equilibrium volume, cohesive energy, and the bulk modulus) of the α-phase of acetonitrile crystal. The average value of the molecular dipole moment obtained in the α-phase is 5.53 D, corresponding to ca. 40% increase as compared to the dipole moment of an isolated acetonitrile molecule, 3.92 D. The calculated densities of solid and liquid acetonitrile turn out to be 8-10% higher than experimental values. This appears to be caused by an overestimate of the atomic many-body dispersion interaction in the density functional calculations used as input in the parametrization of the potential function.