That’s a very good question.
I don’t think the manipulator it self can be adapted to a specific angle, but rather to a specific face. Try following these steps:
- Have two objects, the one you wish to rotate and one more which will serve as a rotation reference, a Plane would be the best.
- Select the Plane and rotate it in Object Mode so that it assumes the angle you want.
- Select the object you mean to rotate and do a Vertex Parent relation to one of the vertices of the Plane.
- Now jump into Edit Mode of the Plane, select the only poly and change the Orientation of the manipulator to Normal.
- Use the manipulator and check the result.
Maybe this works better with Location and not so good with Rotation. I haven’t tested it.