Polarization measurements of the solar chromospheric lines at high precision are key to present and future solar telescopes for understanding magnetic field structures in the chromosphere. The Sunrise Chromospheric Infrared spectroPolarimeter (SCIP) for Sunrise III is a spectropolarimeter with a polarimetric precision of 0.03 % (1 σ). The key to high-precision polarization measurements using SCIP is a polarization modulation unit that rotates a waveplate continuously at a constant speed. The rotating mechanism is a DC brushless motor originally developed for a future space mission, and its control logic was originally developed for the sounding rocket experiment CLASP. Because of our requirement on a speed of rotation (0.512 s/rotation) that was 10 times faster than that of CLASP, we optimized the control logic for the required faster rotation. Fast polarization modulation is essential for investigating the fine-scale magnetic field structures related to the dynamical chromospheric phenomena. We have verified that the rotation performance can achieve the polarization precision of 0.03 % (1 σ) required by SCIP and such a significant rotation performance is maintained under thermal vacuum conditions by simulating the environment of the Sunrise III balloon flight. The waveplate was designed as a pair of two birefringent plates made of quartz and sapphire to achieve a constant retardation in a wide wavelength range. We have confirmed that the retardation is almost constant in the 770 nm and 850nm wavelength bands of SCIP under the operational temperature conditions.