  The magnetic resonance at 41 meV observed in neutron scattering studies of Y
Ba_2 Cu_3 O_7 holds a key position in the understanding of high-T_c
superconductivity. Within the SO(5) model for superconductivity and
antiferromagnetism, we have calculated the effect of an applied magnetic field
on the neutron scattering cross-section of the magnetic resonance. In the
presence of vortices, the neutron scattering cross-section shows clear
signatures of not only the fluctuations in the superconducting order parameter
\psi, but also the modulation of the phase of \psi due to vortices. In
reciprocal space we find that i) the scattering amplitude is zero at
(pi/a,pi/a), ii) the resonance peak is split into a ring with radius pi/d
centered at (pi/a,pi/a), d being the vortex lattice constant, and consequently,
iii) the splitting pi/d scales with the magnetic field as sqrt{B}.
