Plasmonic nanostructures can enable compact multiplexing of the orbital angular momentum (OAM) of light; however, strong dissipation of the highly localized OAM-distinct plasmonic fields in the near-field region hinders on-chip OAM transmission and processing. Superior transmission efficiency is offered by semiconductor nanowires sustaining highly confined optical modes, but only the polarization degree of freedom has been utilized for their selective excitation. Here we demonstrate that incident OAM beams can selectively excite single-crystalline cadmium sulfide (CdS) nanowires through coupling OAM-distinct plasmonic fields into nanowire waveguides for long-distance transportation. This allows us to build an OAM-controlled hybrid nanowire circuit for optical logic operations including AND and OR gates. In addition, this circuit enables the on-chip photoluminescence readout of OAM-encrypted information. Our results open exciting new avenues not only for nanowire photonics to develop OAM-controlled optical switches, logic gates, and modulators but also for OAM photonics to build ultracompact photonic circuits for information processing.