Einstein
’
s theory of General Relativity implies that energy, i.e., matter, curves space-time and thus
deforms lightlike geodesics, giving rise to gravitational lensing. This phenomenon is well understood in the
case of the Schwarzschild metric and has been accurately described in the past; however, lensing in the Kerr
space-time has received less attention in the literature despite potential practical observational applications.
In particular, lensing in such space is not expressible as the gradient of a scalar potential and as such is a
source of curl-like signatures and an asymmetric shear pattern. In this paper, we develop a differentiable
lensing map in the Kerr metric, reworking and extending previous approaches. By using standard tools of
weak gravitational lensing, we isolate and quantify the distortion that is uniquely induced by the presence
of angular momentum in the metric. We apply this framework to the distortion induced by a Kerr-like
foreground object on a distribution of background of sources. We verify that the new unique lensing
signature is orders of magnitude below current observational bounds for a range of lens configurations.