We investigated a Ti:LiNbO$_3$ based integrated-optic polarization controller with a Ti-indiffused waveguide along the z-axis utilizing the electro-optic effect. The device consists of a first quarter-wave (λ/4) phase-shifter followed by a half-wave(λ/2) and a second quarter-wave(λ/4) wave-plate, which is rotated synchronously with the first quarter-wave phase-shifter. We analyzed the operation principles of the device utilizing cascaded transfer matrices based on Jones matrix and Poincare sphere, simulated driving voltages for various input states of polarization (SOP), and theoretically confirmed transformations from any arbitrary input SOP into any general output SOP.