look for the control template of the ManipulationAdorner, it contains the Path with name RotationPart. Out of the box, this Path has HorizontalAlignment 'Center' and VerticalAlignment 'Top', so just alter it to Center-Center or wherever you'd like it.
Note that you will no be able to use a Style to do this but need to edit the whole control template. Once done, just give it a Key (or do not assign a Key and it will be applied application-wide) and put it in your XAML resources (that is, in Window.Resources or App.Resources).