  We study the geometric response of three-dimensional non-Hermitian
crystalline systems with non-trivial point gap topology. For systems with
four-fold rotation symmetry, we show that in presence of disclination lines
with a total Frank angle which is an integer multiple of $2\pi$, there can be
non-trivial, one-dimensional point gap topology along the direction of
disclination lines. This results in disclination-induced non-Hermitian skin
effects. We extend the recently proposed non-Hermitian field theory approach to
describe this phenomenon as a Euclidean Wen-Zee term. Furthermore, by doubling
a non-Hermitian Hamiltonian to a Hermitian 3D chiral topological insulator, we
show that the disclination-induced skin modes are zero modes of the surface
Dirac fermion(s) in the presence of a pseudo-magnetic flux induced by
disclinations.
