  We construct a spinning particle that reproduces the propagation of the
graviton on those curved backgrounds which solve the Einstein equations, with
or without cosmological constant, i.e. Einstein manifolds. It is obtained by
modifying the N=4 supersymmetric spinning particle by relaxing the gauging of
the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable
Chern-Simons couplings on the worldline. We test it by computing the correct
one-loop divergencies of quantum gravity in D=4.
