  This paper investigates charged particle deflection in a Kerr spacetime
background with a dipole magnetic field, focusing on the equatorial plane and
employing the weak field approximation. We employ the Jacobi-Randers metric to
unify the treatment of the gravitational and electromagnetic effects on charged
particles. Furthermore, we utilize the Gauss-Bonnet theorem to calculate the
deflection angle through curvature integrals. The difference between the
prograde and retrograde deflection angles is linked to the non-reversibility of
metrics and geodesics in Finsler geometry, revealing that this difference can
be considered a Finslerian effect. We analyze the impact of both
gravitomagnetic field and dipole magnetic field on particle motion and
deflection using the Jacobi-Randers magnetic field. The model considered in
this paper exhibits interesting features in the second-order approximation of
($M/b$). When $q\mu=2MaE$, the Jacobi-Randers metric possesses reversible
geodesics, leading to equal prograde and retrograde deflection angles. In this
case, the gravitomagnetic field and dipole magnetic field cancel each other
out, distinguishing it from scenarios involving only the gravitomagnetic field
or the dipole magnetic field. We also explore the magnetic field's impact on
gravitational lensing of charged particles.
