  We initiate a study into the eikonal exponentiation of the amplitude in
impact-parameter space when spinning particles are involved in the scattering.
Considering the gravitational scattering of two spin-1/2 particles, we
demonstrate that the leading eikonal exhibits exponentiation up to
$\mathcal{O}(G^{2})$ in the limit where the spacetime dimension
$D\rightarrow4$. We find this to hold for general spin orientations. The
exponentiation of the leading eikonal including spin is understood through the
unitarity properties at leading order in $\hbar$ of momentum-space amplitudes,
allowing the extension of our results to arbitrary-spin scattering.
