  We adapt ``string-inspired'' worldline techniques to one-loop calculations on
orbifolds, in particular on the $S^1/Z_2$ orbifold. Our method also allows for
the treatment of brane-localized terms, or bulk-brane couplings. For
demonstration, we reproduce the well-known result for the one-loop induced
Fayet-Iliopoulos term in rigidly supersymmetric Abelian gauge theory, and
generalize it to the case where soft supersymmetry breaking mass terms for the
bulk scalar fields are present on the branes.
