  Building upon the worldline effective field theory (EFT) formalism for
spinning bodies developed for the Post-Newtonian regime, we generalize the EFT
approach to Post-Minkowskian (PM) dynamics to include rotational degrees of
freedom in a manifestly covariant framework. We introduce a systematic
procedure to compute the total change in momentum and spin in the gravitational
scattering of compact objects. For the special case of spins aligned with the
orbital angular momentum, we show how to construct the radial action for
elliptic-like orbits using the Boundary-to-Bound correspondence. As a
paradigmatic example, we solve the scattering problem to next-to-leading PM
order with linear and bilinear spin effects and arbitrary initial conditions,
incorporating for the first time finite-size corrections. We obtain the
aligned-spin radial action from the resulting scattering data, and derive the
periastron advance and binding energy for circular orbits. We also provide the
(square of the) center-of-mass momentum to ${\cal O}(G^2)$, which may be used
to reconstruct a Hamiltonian. Our results are in perfect agreement with the
existent literature, while at the same time extend the knowledge of the PM
dynamics of compact binaries at quadratic order in spins.
