  The magnetic response expected from a state characterized by rotating
antiferromagnetism in a neutron-scattering experiment is calculated. We predict
the occurrence of a peak at the frequency of the rotation of the rotating
antiferromagnetic order parameter. The doping dependence of this frequency is
very similar to that of the frequency of the magnetic resonance observed in the
neutron-scattering experiments for the hole-doped high-$T_C$ cuprates. This
leads us to propose the rotating antiferromagnetism as a possible mechanism for
this magnetic resonance. We conclude that while the magnitude of the rotating
antiferromagnetic order parameter was previously proposed to be responsible for
the pseudogap and the unusual thermodynamic and transport properties, the phase
of the rotating order parameter is proposed here to be responsible for the
unusual magnetic properties of the high-$T_C$ copper-oxide superconductors.
