setTransformOriginPoint

from PyQt4 import QtGui , QtCore
import sys
import math , time

class Window(QtGui.QWidget):
    def __init__(self):
        super(Window , self).__init__()
        self.UI()

    def UI(self):
        layout = QtGui.QGridLayout()
        button = QtGui.QPushButton('Rotate')
        button.clicked.connect(self.polychange)
        button.setCheckable(True)
        self.view = Example()
        layout.addWidget(button , 0 , 0)
        layout.addWidget(self.view , 0 , 1)
        self.setLayout(layout)
        self.show()

    def polychange(self , sender):
        if sender:
            self.view.polyrotate = 1
            self.view.polyf.setFlag(QtGui.QGraphicsItem.ItemIsMovable , False)

        else:
            self.view.degrees = 0
            self.view.polyf.setFlag(QtGui.QGraphicsItem.ItemIsMovable)

class Example(QtGui.QGraphicsView):
    def __init__(self):
        super(Example , self).__init__()
        self.setSceneRect(0 , 0 , 200 , 200)
        self.degrees = 0
        self.polyrotate = 0
        self.polygon = QtGui.QPolygonF([QtCore.QPointF(50 , 50 ) , QtCore.QPointF(100 , 50) , QtCore.QPointF(100 , 100) , QtCore.QPointF(50 , 100)])
        self.polyf = QtGui.QGraphicsPolygonItem(self.polygon)
        self.polyf.setFlag(QtGui.QGraphicsItem.ItemIsMovable)
        self.scene = QtGui.QGraphicsScene()
        self.setScene(self.scene)
        self.scene.addItem(self.polyf)

    def mousePressEvent(self , e):
        super(Example , self).mousePressEvent(e)
        self.x = e.x()
        self.y = e.y()
        if self.polyrotate == 1:
            self.Rotate()

    def Rotate(self):

        self.pverticesx = []
        self.pverticesy = []
        distances = []
        for i in range(4):
            self.pverticesx.append(self.polyf.mapToScene(self.polyf.polygon()[i]).x())
            self.pverticesy.append(self.polyf.mapToScene(self.polyf.polygon()[i]).y())

        x1 = self.x
        y1 = self.y



        for i in range(4):
             distance = math.hypot(self.pverticesx[i] - x1 , self.pverticesy[i] - y1)
             distances.append(distance)
        midpointx = (self.pverticesx[0] +  self.pverticesx[2]) / 2
        midpointy = (self.pverticesy[0] +  self.pverticesy[2]) / 2
        index = distances.index(min(distances))
        pointx = self.pverticesx[index]
        pointy = self.pverticesy[index]
        vector1 = [x1 - midpointx , y1 - midpointy]
        vector2 = [pointx - midpointx , pointy - midpointy]
        num = 0

        for i in [0 , 1]:
            num = num + (vector1[i] * vector2[i])
        den = math.sqrt(sum(map(lambda x : x * x , vector1))) *  math.sqrt(sum(map(lambda x : x * x , vector2)))

        degree = math.degrees(math.acos(num / den))
        self.degrees = degree + self.degrees
        if self.degrees > 360:
            rotation = self.degrees / 360
            self.degrees = self.degrees - (rotation * 360)

        self.polyf.setTransformOriginPoint(midpointx , midpointy)
        self.polyf.setRotation(self.degrees)



if __name__ == '__main__':
    app = QtGui.QApplication(sys.argv)
    we = Window()
    sys.exit(app.exec_())