The first theoretical investigation of the formation of the linearly polarized solar line spectrum of a complex atom, neutral titanium, is presented. The process of formation of line polarization is modeled by simply considering a plane-parallel layer of Ti I atoms illuminated from below by the photospheric radiation field, and accounting for the differential pumping induced in the various magnetic sublevels by the anisotropic radiation field. The calculated line polarization pattern is in good qualitative agreement with reported observations, thus showing that the generation of population imbalances between magnetic sublevels due to the radiation field anisotropy is the basic physical mechanism responsible for the observed polarization pattern in the Fraunhofer spectrum of Ti I. The role of depolarizing collisions on the polarized spectrum of Ti I is also investigated.