  In this paper, we study the geometry of the moduli space of representations
of the fundamental group of the complement of a torus link into an algebraic
group G, an algebraic variety known as the G-character variety of the torus
link. These torus links are a family of links in the 3-dimensional sphere
formed by stacking several copies of torus knots. We develop an intrinsic
stratification of the variety that allows us to relate its geometry with the
one of the underlying torus knot. Using this information, we explicitly compute
the E-polynomial associated to the Hodge structure of these varieties for
$G=SL_2(\mathbb{C})$ and $SL_3(\mathbb{C})$, for an arbitrary torus link,
showing an unexpected relation with the number of strands of the link.
