  The formalism that describes the non-linear growth of the angular momentum L
of protostructures from tidal torques in a Friedmann Universe, as developed in
a previous paper, is extended to include non-Gaussian initial conditions. We
restrict our analysis here to a particular class of non-Gaussian primordial
distributions, namely multiplicative models. In such models, strongly
correlated phases are produced by obtaining the gravitational potential via a
nonlinear local transformation of an underlying Gaussian random field. The
dynamical evolution of the system is followed by describing the trajectories of
fluid particles using second-order Lagrangian perturbation theory. In the
Einstein-de Sitter universe, the lowest-order perturbative correction to the
variance of the linear angular momentum of collapsing structures grows as t^8/3
for generic non-Gaussian statistics, which contrasts with the t^10/3 growth
rate characteristic of Gaussian statistics. This is a consequence of the fact
that the lowest-order perturbative spin contribution in the non-Gaussian case
arises from the third moment of the gravitational potential, which is
identically zero for a Gaussian field. Evaluating these corrections at the
maximum expansion time of the collapsing structure, we find that these
non-Gaussian and non-linear terms can be as high as the linear estimate,
without the degree of non-Gaussianity as quantified by skewness and kurtosis of
the density field being unacceptably large. The results suggest that
higher-order terms in the perturbative expansion may contribute significantly
to galactic spin which contrasts with the straightforward Gaussian case.
