Rotate Board and Components in Altium
View » Board Planning Mode, commands that support interactively
  changing the shape are available in this mode:
  
  
  Redefine Board Shape - select this command to interactively draw a new shape.
  Move Board Vertices - select this command to interactively modify the shape of the board by moving vertices or sliding the edges
  of the shape. 
  Move Board Shape - select this command to move the complete board shape to a new location in the workspace. Note that this command
  only moves the board shape, other objects that have been placed in the
  workspace are not moved. To move the board shape as well as all placed
  objects, select everything to be moved and use the Edit » Move »
  Move Selection command (switch to 2D Layout Mode first). Taken from
  Altium Tech Doc.
  


The Move Board Shape option will allow you to rotate the whole board(without the components) when the Space Bar is pressed. So I would like to correct my comment, this option does exactly what you need.



Nevertheless, the Move Board Vertices is pretty useful too.