  We study the effect of large-scale magnetic fields on the non-axisymmetric
Rossby wave instability (RWI) in accretion discs. The instability develops
around a density bump, which is likely present in the transition region between
the active zone and dead zone of protoplanetary discs. Previous works suggest
that the vortices resulting from the RWI may facilitate planetesimal formation
and angular momentum transport. We consider discs threaded by a large-scale
poloidal magnetic field, with a radial field component at the disc surface.
Such field configurations may lead to the production of magnetic winds or jets.
In general, the magnetic field can affect the RWI even when it is sub-thermal
(plasma $\beta\sim 10$). For infinitely thin discs, the instability can be
enhanced by about 10 percent. For discs with finite thickness, with a radial
gradient of the magnetic field strength, the RWI growth rate can increase
significantly (by a factor of $\sim 2$) as the field approaches equipartition
($\beta \sim 1$). Our result suggests that the RWI can continue to operate in
discs that produce magnetic winds.
