This article presents the implementation of on-chip iontronic circuits via small-scale integration of multiple ionic logic gates made of bipolar polyelectrolyte diodes. These ionic circuits are analogous to solid-state electronic circuits, with ions as the charge carriers instead of electrons/holes. We experimentally characterize the responses of a single fluidic diode made of a junction of oppositely charged polyelectrolytes (i.e., anion and cation exchange membranes), with a similar underlying mechanism as a solid-state p- and n-type junction. This served to carry out predesigned logical computations in various architectures by integrating multiple diode-based logic gates, where the electrical signal between the integrated gates was transmitted entirely through ions. The findings shed light on the limitations affecting the number of logic gates that can be integrated, the degradation of the electrical signal, their transient response, and the design rules that can improve the performance of iontronic circuits.