  Flourescent iron line profiles currently provide the best diagnostic for
active galactic nuclei (AGN) engine geometries. Here we construct a method for
calculating the relativistic iron line profile from an arbitrarily warped
accretion disc, illuminated from above and below by hard X-ray sources. This
substantially generalises previous calculations of reprocessing by accretion
discs by including non-axisymmetric effects. We include a relativistic
treatment of shadowing by ray-tracing photon paths along Schwarzchild
geodesics. We apply this method to two classes of warped discs, and generate a
selection of resulting line profiles. New profile features include the
possibility of sharper red, and softer blue fall-offs, a time varying line
profile if the warp precesses about the disc, and some differences between
`twisted' and `twist-free' warps. We discuss some qualitative implications of
the line profiles in the context of Type I and II Seyfert AGN.
