Can a herniated disc cause pelvic rotation?

Similar, yes. A ruptured disc which is focalized to right or left will result in focal muscle spasm over the paraspinals. This localized muscle tightness creates asymmetrical net back flexion and extension where the back and pelvic relationships are literally torqued inappropriately, and can create a feeling of rotation, but usually the pain is the focus.
If the disc . Herniation is causing a muscle spasm it can cause the pelvis to tilt or rotate to help keep pressure of the disc herniation of the nerve tissue. This is called a sciatic shift or spasmodic scoliosis .