Integrated photonics is a remarkable platform for the realization of quantum computations due to its flexibility and scalability. Here we propose a novel paradigm exploiting twisted waveguides as a building block for polarization-encoded quantum photonic computations on a chip. We unveil a transformation (gate) matrix in the closed form and demonstrate that twisted waveguides can implement arbitrary Bloch sphere rotations. The outcomes of this research may open a new direction in the development of quantum computing architectures on a chip.