The vorticity vector of the current density J^B, induced in the electron cloud of a molecule by a magnetic field B, is defined by V^B = ∇ × J^B. The vorticity tensor is the nonsymmetric second-rank tensor obtained by differentiating the vorticity vector with respect to the components of B, i.e., . It is shown that isosurfaces of its anisotropy can be used as magnetotropicity indicators to detect electron delocalization effects and estimate the degree of aromaticity of cyclic molecules on the magnetic criterion.