  We consider the motion of classical spinning test particles in Schwarzschild
and Kerr metrics and investigate innermost stable circular orbits (ISCO). The
main goal of this work is to find analytically the small-spin corrections for
the parameters of ISCO (radius, total angular momentum, energy, orbital angular
frequency) of spinning test particles in the case of vectors of black hole
spin, particle spin and orbital angular momentum being collinear to each other.
We analytically derive the small-spin linear corrections for arbitrary Kerr
parameter $a$. The cases of Schwarzschild, slowly rotating and extreme Kerr
black hole are considered in details. For a slowly rotating black hole the ISCO
parameters are obtained up to quadratic in $a$ and particle's spin $s$ terms.
From the formulae obtained it is seen that the spin-orbital coupling has
attractive character when spin and angular momentum are parallel and repulsive
when they are antiparallel. For the case of the extreme Kerr black hole with
co-rotating particle we succeed to find the exact analytical solution for the
limiting ISCO parameters for arbitrary spin. It has been shown that the
limiting values of ISCO radius and frequency do not depend on the particle's
spin while values of energy and total angular momentum depend on it. We have
also considered circular orbits of arbitrary radius and have found small-spin
linear corrections for the total angular momentum and energy at given radius.
System of equations for numerical calculation of ISCO parameters for arbitrary
$a$ and $s$ is also explicitly written.
