If you want a bit finer control over the rotation, you can follow this convoluted set of steps: That being said, after you select the graphic (again, using the mouse) you could use the Alt key, in conjunction with the left and right arrow keys, to rotate the graphic in 15-degree increments in the direction consistent with the arrow key used.
If you've just clicked on the graphic to select it, your mouse pointer is already very close to the rotation handle, so you might as well use it to do the rotation. The short answer is "not really." The reason for this is because before you can rotate a graphic you need to select it, and selecting can only be done (as far as I can tell) by using the mouse. He wonders, though, if there is a way to rotate a graphic using nothing but the keyboard. Don knows how to rotate a graphic using the mouse.