  We generalize to the Kerr spacetime existing self-force results on tidal
invariants for particles moving along circular orbits around a Schwarzschild
black hole. We obtain linear-in-mass-ratio corrections to the quadratic and
cubic electric-type invariants and the quadratic magnetic-type invariant in
series of the rotation parameter up to the fourth order. We then construct the
eigenvalues of both electric and magnetic tidal tensors and analytically
compute them through high post-Newtonian orders.
