  In this short note we give a characterization of smooth projective varieties
of Picard number one that are separably uniruled but not separably rationally
connected. We also give a sufficient condition involving the torsion order and
the uniruling index for a smooth Fano variety of Picard number one to be
separably rationally connected. As an application, we prove some weak
approximation results for Fano complete intersections in positive
charactersitic. For example, we show that weak approximation holds at place of
strong potentially good reduction for a Fano complete intersection in
$\mathbb{P}^n$ of type $(d_1, \ldots, d_c)$ in characteristic $p$ such that
$n>d_1+\ldots +d_c, p>d_1, \ldots, d_c.$
