  An external Abelian magnetic field excites in the QCD vacuum a tensor
supercurrent that represents the tensor polarization of the chiral condensate.
This tensor supercurrent can be deduced from the chiral lagrangian in the
presence of anomalies; a similar tensor supercurrent emerges in rotating
systems at finite chemical potential. We discuss the microscopic origin of this
supercurrent and argue that it screens the instanton--anti-instanton $I\bar{I}$
molecules in the QCD vacuum, similarly to the vector supercurrent screening
Abrikosov vortices in a superconductor. A number of possible experimental
manifestations of the tensor supercurrent are discussed: {\it i}) spin
alignment of axial-vector and vector mesons in heavy ion collisions; {\it ii})
tensor charge of the nucleon; {\it iii}) transversity of quark distributions in
polarized nucleons.
