In this brief article we summarize the derivation of the Sivers function of a heavy nucleus, which we obtain by generalizing the quasi-classical McLerran-Venugopalan model to incorporate the role of spin and orbital angular momentum. In doing so we obtain a new channel which is capable of generating the Sivers function of the nucleus from the orbital motion of its nucleons. An essential role is played in this channel by the multiple rescatterings on spectator nucleons which screen the distribution function during the initial- or final-state interactions. The combination of orbital angular momentum together with multiple rescattering yields a new interpretation of the sign flip relation between the Sivers function measured in semi-inclusive deep inelastic scattering and the Drell-Yan process.