  Given a graded ample Hausdorff groupoid, we realise its graded Steinberg
algebra as a partial skew inverse semigroup ring. We use this to show that for
a partial action of a discrete group on a locally compact Hausdorff topological
space, the Steinberg algebra of the associated groupoid is graded isomorphic to
the corresponding partial skew group ring. We show that there is a one-to-one
correspondence between the open invariant subsets of the topological space and
the graded ideals of the partial skew group ring. We also consider the
algebraic version of the partial $C^{*}$-algebra of an abelian group and
realise it as a partial skew group ring via a partial action of the group on a
topological space. Applications to the theory of Leavitt path algebras are
given.
