I have a shape in a sketch that I'd like to rotate 180 degrees (effectively around the Z axis).
As bejant says, there are several ways to interpret that statement, but I'd guess that you mean it is in the XY plane and you want to rotate about the normal to that plane, ie the z axis.
Look at Placement , you will find axis z has a value of 1 and x,y are zero. set angle to 180 and I think you will get what you are trying to do.
If that is not the right guess please attach your fcstd file or give a fuller, non ambiguous description.