We investigate the dynamics of a millimetre-sized air bubble rising in a liquid due to buoyancy under the influence of a magnetic field applied in a direction transverse to the bubble motion by conducting three-dimensional numerical simulations. The path and trajectory of the air bubble are examined by varying the strength of the transverse magnetic field. In the absence of a magnetic field, it is well known that under certain conditions a tiny air bubble undergoes spiralling motion due to its shape deformation and vortex shedding in the wake region. It is shown here that the spiralling motion of an air bubble observed without magnetic field transforms into a purely zigzagging motion under an applied transverse magnetic field. To understand the mechanism, we analyse the evolution of the wake vortices and forces experienced by the bubble in the presence of a transverse magnetic field. It is found that the twisted double-threaded vortices observed in a spiralling bubble in the absence of a magnetic field appear to rotate perpendicularly to the applied magnetic field across the vertical axis, thereby making the bubble shift its trajectory from spiralling to zigzagging. By calculating the lift and drag forces acting on the bubble, it is shown that how these forces acting on the bubble contribute to the vortex shedding patterns. Thus, the present study demonstrates the mechanism to control the trajectory of an air bubble under the application of a magnetic field. © 2020