  In this paper the problem of gravitational deflection of relativistic charged
massive particles in slowly rotating Kerr-Newman black holes is considered.
Toward this purpose we have used two methods: Firstly, we have applied the
Gauss-Bonnet theorem (GBT) and the optical geometry to evaluate the deflection
angle of charged particles. Secondly, we have presented a detailed analysis of
the deflection angle by means of the Hamilton-Jacobi equation recovering the
same invariant result for the deflection angle in leading order terms. The
crucial point behind the first method is to use the correspondence between the
motion of a charged massive particles in a gravitational field in presence of
electromagnetic field and the motion of photons in a non-homogeneous cold
plasma. It is shown that the deflection angle besides the black hole (BH) mass
$M$, BH angular momentum $a$, BH electric charge $Q^2$, BH magnetic charge
$P^2$, it is also affected by the electric charge of the particle $q$ and
relativistic velocity of the particle $v$.
