  We consider the motion of a point particle with spin in a stationary
spacetime. We define, following Witzany (2019) and later Ramond (2022), a
twelve dimensional Hamiltonian dynamical system whose orbits coincide with the
solutions of the Mathisson-Papapetrou-Dixon equations of motion with the
Tulczyjew-Dixon spin supplementary condition, to linear order in spin. We then
perturb this system by adding the conservative pieces of the leading order
gravitational self-force and self-torque sourced by the particle's mass and
spin. We show that this perturbed system is Hamiltonian and derive expressions
for the Hamiltonian function and symplectic form. This result extends our
previous result for spinless point particles.
