  We study QCD finite energy sum rules (FESR) for the axial-vector current
correlator in the presence of a magnetic field, in the weak field limit and at
zero temperature. We find that the perturbative QCD as well as the hadronic
contribution to the sum rules get explicit magnetic field-dependent corrections
and that these in turn induce a magnetic field dependence on the deconfinement
phenomenological parameter s_0 and on the gluon condensate. The leading
corrections turn out to be quadratic in the field strength. We find from the
dimension d=2 first FESR that the magnetic field dependence of s_0 is
proportional to the absolute value of the light-quark condensate. Hence, it
increases with increasing field strength. This implies that the parameters
describing chiral symmetry restoration and deconfinement behave similarly as
functions of the magnetic filed. Thus, at zero temperature the magnetic field
is a catalysing agent of both chiral symmetry breaking and confinement. From
the dimension d=4 second FESR we obtain the behavior of the gluon condensate in
the presence of the external magnetic field. This condensate also increases
with increasing field strength.
