Currently, the only way of changing pivot for rotation is by setting "Local Rotate Pivot".
1- Create a Box (its pivot is at 0,0,0 by default)
2- Go to Transform -> Pivots panel and set "Local Rotate Pivot" to ( -0.5 ,0, 0).
3- Now if you rotate the box, it rotates around left side of box (like a door)
Note that you may stay in Move manipulator mode while changing pivot, so you can see the changes in viewport.
More methods of setting pivots will come to Clara.io, so you can later go into a pivot edit mode and position the pivot.