In this paper, a controllable hybrid plasmonic integrated circuit (CHPIC) composed of hybrid plasmonic waveguide (HPW)-based rhombic nano-antenna, polarization beam splitter, coupler, filter, and sensor has been designed and investigated for the first time. In order to control the power into a corresponding input port, a graphene-based 1 × 3 power splitter with switchable output has been exploited. The functionality of each device has been studied comprehensively based on the finite element method and the advantages over state-of-the-art have been compared. Moreover, the effect of connection of CHPIC to the photonic and plasmonic waveguides has been studied to exhibit the capability of variety excitation methods of the CHPIC. Furthermore, the performance of the proposed CHPIC connected to inter/intra wireless transmission links has been investigated. The wireless transmission link consists of two HPW-based nano-antennas as transmitter and receiver with the maximum gain and directivity of 10 dB and 10.2 dBi, respectively, at 193.5 THz. The suggested CHPIC can be used for applications such as optical wireless communication and inter/intra-chip optical interconnects.