  We compute the rotations, during a scattering encounter, of the spins of two
gravitationally interacting particles at second-order in the gravitational
constant (second post-Minkowskian order). Following a strategy introduced in
Phys. Rev. D {\bf 96}, 104038 (2017), we transcribe our result into a
correspondingly improved knowledge of the spin-orbit sector of the Effective
One-Body (EOB) Hamiltonian description of the dynamics of spinning binary
systems. We indicate ways of resumming our results for defining improved
versions of spinning EOB codes which might help in providing a better
analytical description of the dynamics of coalescing spinning binary black
holes.
