Can I move the center of rotation in dataset alignment?

You cannot move the position of the marker, but you can select another dataset as the reference dataset.

The dataset rotates according to the center of rotation, which is the white marker in in the screenshot below. The position of the marker is defined by the mapping start point of the reference dataset (the one selected with the "star" marker). You cannot move the marker, but you can select another dataset as the reference dataset.