  The field theoretic renormalization group and the operator product expansion
are applied to the stochastic model of passively advected vector field with the
most general form of the nonlinear term allowed by the Galilean symmetry. The
advecting turbulent velocity field is governed by the stochastic Navier--Stokes
equation. It is shown that the correlation functions of the passive vector
field in the inertial range exhibit anomalous scaling behaviour. The
corresponding anomalous exponents are determined by the critical dimensions of
tensor composite fields (operators) built solely of the passive vector field.
They are calculated (including the anisotropic sectors) in the leading order of
the expansion in $y$, the exponent entering the correlator of the stirring
force in the Navier--Stokes equation (one-loop approximation of the
renormalization group). The anomalous exponents exhibit an hierarchy related to
the degree of anisotropy: the less is the rank of the tensor operator, the less
is its dimension. Thus the leading terms, determined by scalar operators, are
the same as in the isotropic case, in agreement with the Kolmogorov's
hypothesis of the local isotropy restoration.
