In photonic systems, bilayer or multilayer systems exhibit numerous exciting phenomena induced by twisting. Thus, it is highly desired to explore the twisting effect by engineering the light-matter interactions. Optical torque, an important means in optical micromanipulation, can rotate micro-objects in various ways, enabling a wide range of promising applications. In this study, we present an interesting phenomenon called "pure optical twist" (POT), which emerges when a bilayer structure with specific symmetry is illuminated by counter-propagating lights with opposite spin and/or orbital angular momentum. Remarkably, this leads to zero net optical torque but yet possesses an interesting mechanical effect of bilayer system twisting. The crucial determinant of this phenomenon is the rotational symmetries of each layer, which govern the allowed azimuthal channels of the scattered wave. When the rotational symmetries do not allow these channels to overlap, no resultant torque is observed. Our work will encourage further exploration of the twisting effect through engineered light-matter interactions. This opens up the possibility of creating twisted bilayer systems using optical means, and constructing a stable bilayer optical motor that maintains identical rotation frequencies for both layers.