Rotate rectangle around its center

 void paintEvent(QPaintEvent* event){
    QPainter painter(this);

    // xc and yc are the center of the widget's rect.
    qreal xc = width() * 0.5;
    qreal yc = height() * 0.5;

    painter.setPen(Qt::black);

    // draw the cross lines.
    painter.drawLine(xc, rect().top(), xc, rect().bottom());
    painter.drawLine(rect().left(), yc, rect().right(), yc);

    painter.setBrush(Qt::white);
    painter.setPen(Qt::blue);

    // Draw a 13x17 rectangle rotated to 45 degrees around its center-point
    // in the center of the canvas.

    // translates the coordinate system by xc and yc
    painter.translate(xc, yc);

    // then rotate the coordinate system by 45 degrees
    painter.rotate(45);

    // we need to move the rectangle that we draw by rx and ry so it's in the center.
    qreal rx = -(13 * 0.5);
    qreal ry = -(17 * 0.5);
    painter.drawRect(QRect(rx, ry, 13, 17));
  }

You are in the painter's coordinate system. When you call drawRect(x, y, 13, 17), it's upper left corner is at (x,y). If you want (x, y) to be the center of your rectangle, then you need to move the rectangle by half, hence rx and ry.

You can call resetTransform() to reset the transformations that were made by translate() and rotate().

Simple:

void rotate(QPainter* p, const QRectF& r, qreal angle, bool clock_wise) {
    p->translate(r.center());
    p->rotate(clock_wise ? angle : -angle);
    p->translate(-r.center());
}