Setting an upper limit or detection of B-mode polarization imprinted by gravitational waves from Inflation is one goal of modern large angular scale cosmic microwave background (CMB) experiments around the world. A great effort is being made in the deployment of many ground-based, balloon-borne and satellite experiments, using different methods to separate this faint polarized component from the incoming radiation. QUBIC exploits one of the most widely-used techniques to extract the input Stokes parameters, consisting in a rotating half-wave plate (HWP) and a linear polarizer to separate and modulate polarization components. QUBIC uses a step-by-step rotating HWP, with 15° steps, combined with a 0.4°s-1 azimuth sky scan speed. The rotation is driven by a stepper motor mounted on the cryostat outer shell to avoid heat load at internal cryogenic stages. The design of this optical element is an engineering challenge due to its large 370 mm diameter and the 8 K operation temperature that are unique features of the QUBIC experiment. We present the design for a modulator mechanism for up to 370 mm, and the first optical tests by using the prototype of QUBIC HWP (180 mm diameter). The tests and results presented in this work show that the QUBIC HWP rotator can achieve a precision of 0.15° in position by using the stepper motor and custom-made optical encoder. The rotation induces <5.0 mW (95% C.L) of power load on the 4 K stage, resulting in no thermal issues on this stage during measurements. We measure a temperature settle-down characteristic time of 28 s after a rotation through a 15° step, compatible with the scanning strategy, and we estimate a maximum temperature gradient within the HWP of ≤ 10 mK. This was calculated by setting up finite element thermal simulations that include the temperature profiles measured during the rotator operations. We report polarization modulation measurements performed at 150 GHz, showing a polarization efficiency >99% (68% C.L.) and a median cross-polarization χPol of 0.12%, with 71% of detectors showing a χPol + 2σ upper limit <1%, measured using selected detectors that had the best signal-to-noise ratio.