It's impossible to rotate a circle - at least in computer graphics terms where a circle is defined by its center-point and a radius. I would do the following: store your circle-with-a-line-in-it as a class, give it two vectors as members, one for its center-point and one to represent its orientation. Then when you draw this construct you draw the circle (without rotation of any kind, that doesn't make sense - use the construct's center-point vector member as the origin of the circle obviously) and then you determine a line from the center of your circle out into the direction the whole thing is pointing (using the second member vector, the orientation) and just draw a segment (a part) of that line.
This is what you would get, the small red line is your orientation member vector which would not be drawn, instead the small thick black segment of it is drawn.
Hope this makes sense and helps.