  This paper studies the deflection of charged particles in a dipole magnetic
field in Schwarzschild spacetime background in the weak field approximation. To
calculate the deflection angle, we use Jacobi metric and Gauss-Bonnet theorem.
Since the corresponding Jacobi metric is a Finsler metric of Randers type, we
use both the osculating Riemannian metric method and generalized Jacobi metric
method. The deflection angle up to fourth order is obtained and the effect of
the magnetic field is discussed. It is found that the magnetic dipole will
increase (or decrease) the deflection angle of a positively charged signal when
its rotation angular momentum is parallel (or antiparallel) to the magnetic
field. It is argued that the difference in the deflection angles of different
rotation directions can be viewed as a Finslerian effect of the
non-reversibility of the Finsler metric. The similarity of the deflection angle
in this case with that for the Kerr spacetime allows us to directly use the
gravitational lensing results in the latter case. The dependence of the
apparent angles on the magnetic field suggests that by measuring these angles
the magnetic dipole might be constrained.
