We investigate the ordering mechanism of the striped pattern of a binary mixture in the presence of periodic oscillatory particles with a special addictive to one of the two immiscible phases. Due to the presence of oscillatory particles, the phase separation of the system will be significantly perturbed, and composition fluctuations are suppressed anisotropically. By changing the oscillatory frequency omega and amplitude gamma, we observe the striped domain structures either parallel or perpendicular to the oscillatory direction, and obtain a gamma-omega phase diagram describing the orientational ordering of the phase-separating structures. The results suggest that our model system may provide a novel and simple way to control the ordering morphology of soft materials.