We make a simple electrically controllable linear polarization rotator over $360^{circ}$ without loss by using a thick ECB(electrically controlled birefringence) liquid crystal cell and a quarter wave plate at 514.5 nm wavelength. Its operating principle can be analyzed and explained by using simple polarization analysis and experimental data. We demonstrate that the degree of polarization of the rotator is 0.964 and the temporal variation for 1 week lies within ${pm}1$ degree. We can easily solve the problem of nonlinearity of the dependence of the rotational angle of linear polarization on the applied voltage by changing the utilized voltage range or its fitting curve.