This article deals with the problem of an isolated, rigid inclusion with linear-magnetic behavior embedded in a linear-elastic matrix. Under the hypothesis of infinitesimal deformations, an analytical expression is obtained for the equilibrium rotation of the magnetic inclusion under general magneto-mechanical loading conditions. The results show that the inclusion undergoes an ‘extra’ rotation due to the presence of non-aligned magnetic fields (even in the absence of mechanical loadings). Moreover, this extra rotation is found to depend on the shape of the inclusion, as well as on its magnetic anisotropy. Thus, the extra rotation increases monotonically to an asymptote with increasing magnetic anisotropy of the inclusion, while, for fixed magnetic behavior of the inclusion, the extra rotation increases up to a maximum with increasing aspect ratio, and then decays to zero.