I would add three buttons to the UI:

One that shows an arrow that points to an empty rectangle (move to free tile).
One that shows an circulair arrow pointing clockwise
One that shows an circulair arrow pointing counter-clockwise

The user should click one of these buttons to select the corresponding action, and then click a tile. This would make the UI easier to use because the user can see what he is doing. It requires more click's though. :?

Another very easy-to-use approach:

Left-click is Move to free.
Right-click is Rotate (CCW or CW).

I think you don't need both clockwise and counterclockwise rotations. Rotating 90 degrees counterclockwise is the same as rotating 270 degrees clockwise right?