  We study the influence of a background magnetic field on the $J/\psi$ vector
meson in a DBI-extension of the soft wall model, building upon our earlier work
Phys. Rev. D91, 086002 (2015). In this specific holographic QCD model, we
discuss the heavy quark number susceptibility and diffusion constants of charm
quarks and their dependence on the magnetic field by either a hydrodynamic
expansion or by numerically solving the differential equation. This allows us
to determine the response of these transport coefficients to the magnetic
field. The effects of the latter are considered both from a direct as indirect
(medium) viewpoint. As expected, we find a magnetic field induced anisotropic
diffusion, with a stronger diffusion in the longitudinal direction compared to
the transversal one. We backup, at least qualitatively, our findings with a
hanging string analysis of heavy quark diffusion in a magnetic field. From the
quark number susceptibility we can extract an estimate for the effective
deconfinement temperature in the heavy quark sector, reporting consistency with
the phenomenon of inverse magnetic catalysis.
