  We investigate the scattering of a spinning test particle by a Kerr black
hole within the Mathisson-Papapetrou-Dixon model to linear order in spin. The
particle's spin and orbital angular momentum are taken to be aligned with the
black hole's spin. Both the particle's mass and spin length are assumed to be
small in comparison with the characteristic length scale of the background
curvature, in order to avoid backreaction effects. We analytically compute the
modifications due to the particle's spin to the scattering angle, the
periastron shift, and the condition for capture by the black hole, extending
previous results valid for the nonrotating Schwarzschild background. Finally,
we discuss how to generalize the present analysis beyond the linear
approximation in spin, including spin-squared corrections in the case of a
black-hole-like quadrupolar structure for the extended test body.
