  We study the binary dynamics of two Kerr black holes with arbitrary spin
vectors in the presence of parity-even and parity-odd cubic deformations of
gravity. We first derive the tree-level Compton amplitudes for a Kerr black
hole in cubic gravity, which we then use to compute the two-to-two amplitudes
of the massive bodies to leading order in the deformation and the
post-Minkowskian expansion. The required one-loop computations are performed
using the leading singularity approach as well as the heavy-mass effective
field theory (HEFT) approach. These amplitudes are then used to compute the
leading-order momentum and spin kick in cubic gravity in the KMOC formalism.
Our results are valid for generic masses and spin vectors, and include all the
independent parity-even and parity-odd cubic deformations of Einstein-Hilbert
gravity. We also present spin-expanded expressions for the momentum and spin
kicks, and the all-order in spin deflection angle in the case of aligned spins.
