A 2×2 cross/bar polymer electro-optic (EO) routing switch is proposed, which is composed of two passive channel waveguides and two active EO polymer microrings with bending radius of only 13.76 μm. Detailed structure, theory and formulation are provided to characterize the output power of the switch. For obtaining fundamental mode propagation, small bending loss and phase-matching between channel waveguide and microring resonator (MRR) waveguide, the structural parameters are optimized under the wavelength of 1550 nm. Analyses and simulations on output power and output spectra indicate that a switching voltage of 5 V is desired to realize the exchange between cross state and bar state, the crosstalk under cross state and that under bar state are about -28.8 dB and -39.9 dB, respectively, and the insertion losses under these two states are about 2.42 dB and 0.13 dB, respectively. Compared with our four EO switches reported before, this device possesses ultra-compact size of 0.233 mm×0.233 mm as well as low crosstalk and insertion loss, and therefore it can serve as a good candidate for constructing large-scale optical routers or switching arrays in photonic network-on-chip (NoC).