We propose an ultra-compact electro-optic microring modulator based on a hybrid plasmonic waveguide. In comparison to previously proposed structures, the present structure utilizes aluminum-doped zinc oxide (AZO), rather than noble metals, for plasmon excitation. AZO can be used to simultaneously tune both the real and imaginary parts of the dielectric constant by changing the carrier concentration. The modulation depth and insertion loss of the microring modulator are 18.70 and 2.76 dB. The proposed modulator has a high modulation speed because its capacitance is 0.22 fF. This device could be used in high-density integrated optical circuits.