Electro-optic (EO) modulators are vital for efficient "electrical to optical" transitions and high-speed optical interconnects. In this work, we applied an EO polymer to demonstrate modulators on silicon-on-insulator substrates. The fabricated Mach-Zehnder interferometer (MZI) and ring resonator consist of a Si and TiO2 slot, in which the EO polymer was embedded to realize a low-driving and large bandwidth modulation. The designed optical and electrical constructions are able to provide a highly concentrated TM mode with low propagation loss and effective EO properties. The fabricated MZI modulator shows a π-voltage-length product of 0.66 V·cm and a 3-dB bandwidth of 31 GHz. The measured EO activity is advantageous to exploit the ring modulator with a resonant tunability of 0.065 nm/V and a 3-dB modulation bandwidth up to 13 GHz.