  We investigate the effects of non-Gaussianity in the primordial density field
on the reionization history. We rely on a semi-analytic method to describe the
processes acting on the intergalactic medium (IGM), relating the distribution
of the ionizing sources to that of dark matter haloes. Extending previous work
in the literature, we consider models in which the primordial non-Gaussianity
is measured by the dimensionless non-linearity parameter f_NL, using the
constraints recently obtained from cosmic microwave background data. We predict
the ionized fraction and the optical depth at different cosmological epochs
assuming two different kinds of non-Gaussianity, characterized by a
scale-independent and a scale-dependent f_NL and comparing the results to those
for the standard Gaussian scenario. We find that a positive f_NL enhances the
formation of high-mass haloes at early epochs, when reionization begins, and,
as a consequence, the IGM ionized fraction can grow by a factor up to 5 with
respect to the corresponding Gaussian model. The increase of the filling factor
has a small impact on the reionization optical depth and is of order ~ 10 per
cent if a scale-dependent non-Gaussianity is assumed. Our predictions for
non-Gaussian models are in agreement with the latest WMAP results within the
error bars, but a higher precision is required to constrain the scale
dependence of non-Gaussianity.
