The action of a magnetic field on the behavior of a bulk dust cluster formed in the strata of a glowing discharge has been studied. The cluster that consists of seven chains of particles and is a hexagonal cell in the horizontal cross-section has been studied. It has been found that the rotation of a dust cluster arises in nonzero magnetic field unlike the dusty structure containing many particles in the horizontal cross-section. Moreover, it has been found that the threshold behavior of the occurrence of rotation in the cluster is affected by the discharge current and plasma-forming gas pressure. The enhancement of the ionization inside a dust cluster is suggested as an interpretation. The radial ion flux that moves in the longitudinal magnetic field from the dusty structure to the discharge tube wall additionally twists the structure with the negative projection of an angular velocity on the magnetic induction vector.