A new method has been demonstrated using a polarized deuteron beam in the storage ring COSY to search for axion-like particles. The signal would be a resonant jump in the vertical polarization component of a polarized beam whose spins are rotating in the ring plane under the influence of the COSY bending magnets. The axion would cause the electric dipole moment (EDM) of the beam particles to oscillate. If this frequency happens to coincide with the polarization rotation rate in the ring plane during a scan of the beam momentum, then the torques on the polarization induced through the EDM by the radial electric field in the beam frame will accumulate, leading to a change in the vertical polarization component. In the spring of 2019, we used a 0.97-GeV/c vector-polarized deuteron beam to successfully demonstrate the procedure for the search. The phase of the oscillating EDM with respect to the rotation of the polarized beam is unknown. In order to be sensitive to both cosine and sine components of the oscillation, we prepared four beam bunches for the ring with different polarization directions. Starting with vertical polarization following injection into the ring, an RF solenoid operating on the (1 + Gγ) harmonic of the beam revolution frequency was used to rotate the polarization into the horizontal plane. This yielded a polarization pattern in which two of the bunches had polarizations that were nearly orthogonal. By looking separately for signals on both bunches, a signal would be found for any value of the axion phase. Beam polarizations were measured using the WASA Forward Detector. In order to improve the horizontal polarization lifetime, the beam was electron cooled as well as bunched. Once the orbit was established with minimal steering corrections, the ring sextupole magnets were adjusted to maximize the horizontal polarization lifetime. All scans were made with lifetimes in excess of 500 s. The sensitivity to an axion was tested and calibrated using an RF Wien filter with a horizontal magnetic field to create vertical polarization jumps during a momentum scan of COSY. In a series of scans spanning a 1.2% change in the neighborhood of 121 kHz spin tune frequency (associated with the axion mass), no signals were seen that did not fit the statistical distribution that arises from event counting data collection.