We propose a method for selectively propagating optical vortex modes with specific charge numbers in a photonic integrated circuit (PIC) by using a topological photonic system. Specifically, by performing appropriate band tuning in two photonic structures that comprise a topological waveguide, one specific electromagnetic mode at the Γ point of a band diagram can be excited. Based on theoretical analysis, we successfully propagated optical vortex modes with specific charge numbers over a wide range in the C band in the proposed topological waveguide. The proposed method could be useful in controlling optical vortex signals at the chip level in future orbital angular momentum multiplexing technologies.