The Format Text dialogue for Leader Text can be quite misleading. There is an apparent option to rotate the text, but it is always greyed out. This is because the form of the dialogue mirrors the standard Text dialogue box where it is an actual option.
In order to rotate leader text you need to edit the Dimension Style
Leader text alignment is not controlled by the Leader tree in the Styles Editor, but is found in the end tab in the Dimension tree:
Change the selection of the Leader Text Orientation drop-down box to "Aligned", as shown in the picture above. Remember to save the style, and save it to the library if you want to use it globally across Inventor.
Now when you place a leader, make sure you place at least two line segments after the insertion point, as it is the end vertex of the second segment that can be used to rotate the leader text into the desired position:
This method should suffice for most situations, but if you require more options then look into creating a Sketched Symbol in your drawing, and save it to the template if you wish to re-use it across new drawings.
Peter Barker also reminded me to mention that whilst this works for leaders there are similar settings available to rotate text for Linear, Diameter and Radius Dimensions as shown in the following image.