  In this paper, we investigate the deflection of a charged particle moving in
the equatorial plane of Kerr-Newman spacetime, focusing on weak field limit. To
this end, we use the Jacobi geometry, which can be described in three
equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem,
and $(n+1)$-dimensional stationtary spacetime picture. Based on Randers data
and Gauss-Bonnet theorem, we utilize osculating Riemannian manifold method and
the generalized Jacobi metric method to study the deflection angle,
respectively. In the $(n+1)$-dimensional spacetime picture, the motion of
charged particle follows the null geodesic, and thus we use the standard
geodesic method to calculate the deflection angle. Three methods lead to the
same second-order deflection angle, which is obtained for the first time. The
result shows that the black hole spin $a$ affects the deflection of charged
particles both gravitationally and magnetically at the leading order (order
$\mathcal{O}([M]^2/b^2)$). When $qQ/E<2M$, $a$ will decrease (or increase) the
deflection of prograde (or retrograde) charged signal. If $qQ/E> 2M$, the
opposite happens, and the ray is divergently deflected by the lens. We also
showed that the effect of the magnetic charge of the dyonic Kerr-Newman black
hole on the deflection angle is independent of the particle's charge.
