You can move a roundabout by selecting the centerpoint of the roundabout, and dragging it.
If you move the base alignment that a roundabout approach road was created from, the roundabout components remain dynamic to the base alignment, and move with the base alignment.
If you need to change the centerpoint location of a roundabout, you can do it by deleting the roundabout, recreating the roundabout, and selecting a new roundabout center point location.