  A possible experimental observation of the chiral magnetic effect in heavy
ion collisions at RHIC was recently reported by the STAR Collaboration. We
study signatures of this effect in SU(2) lattice gluodynamics with the chirally
invariant Dirac operator. We find that at zero temperature the local
fluctuations of an electric current of quarks and chirality fluctuations
increase with external Abelian magnetic field. The external magnetic field
leads to spatial separation of the quark's electric charges. The separation
increases with the strength of the magnetic field. As temperature gets higher
the dependence of these quantities on the strength of the magnetic field
becomes weaker. In the deconfinement phase the local fluctuations of the chiral
density and of the spatial components of the quarks electric current are large
and are almost independent on the external magnetic field. The local
fluctuations of the electric charge density decrease with the strength of the
magnetic field in this phase.
