  We use the canonical Hamiltonian formalism to generalize to spinning point
particles the first law of mechanics established for binary systems of
non-spinning point masses moving on circular orbits [Le Tiec, Blanchet, and
Whiting, Phys. Rev. D 85, 064039 (2012)]. We find that the redshift observable
of each particle is related in a very simple manner to the canonical
Hamiltonian and, more generally, to a class of Fokker-type Hamiltonians. Our
results are valid through linear order in the spin of each particle, but hold
also for quadratic couplings between the spins of different particles. The
knowledge of spin effects in the Hamiltonian allows us to compute spin-orbit
terms in the redshift variable through 2.5PN order, for circular orbits and
spins aligned or anti-aligned with the orbital angular momentum. To describe
extended bodies such as black holes, we supplement the first law for spinning
point-particle binaries with some "constitutive relations" that can be used for
diagnosis of spin measurements in quasi-equilibrium initial data.
