We propose a new explanation for the origin of angular momentum in galaxies and their dark halos, in which the halos obtain their spin through the cumulative acquisition of angular momentum from satellite accretion. In our model, the build-up of angular momentum is a random walk process associated with the mass assembly history of the halos major progenitor. We assume no correlation between the angular momenta of accreted objects. Using the extended Press-Schechter approximation, we calculate the growth of mass, angular momentum, and spin parameter $lambda$ for many halos. Our random walk model reproduces the key features of the angular momentum of halos found in N-body simulations: a lognormal distribution in $lambda$ with an average of $<lambda> approx 0.04$, independent of mass and redshift. The evolution of the spin parameter in individual halos in this model is quite different from the steady increase with time of angular momentum in the tidal torque picture. We find both in N-body simulations and in our random walk model that the value of $lambda$ changes significantly with time for a halos major progenitor. It typically has a sharp increase due to major mergers, and a steady decline during periods of gradual accretion of small satellites. The model predicts that on average the $lambda$ of halos which had major mergers after redshift $z=2$ should be substantially larger than the $lambda$ of those which did not. Perhaps surprisingly, this suggests that halos that host late-forming elliptical galaxies should rotate faster than halos of spiral galaxies.
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