  Let $\Delta$ be a simplicial complex of a matroid $M$. In this paper, we
explicitly compute the regularity of all the symbolic powers of a
Stanley-Reisner ideal $I_\Delta$ in terms of combinatorial data of the matroid
$M$. In order to do that, we provide a sharp bound between the arboricity of
$M$ and the circumference of its dual $M^*$.
