You can get halfway there by calling the DrawToBitmap method on your panel, then rotating the bitmap and displaying it e.g. in a PictureBox:
var bitmap = new Bitmap(panel.Width, panel.Height);
panel.DrawToBitmap(bitmap, new Rectangle(Point.Empty, panel.Size));
bitmap.RotateFlip(RotateFlipType.Rotate270FlipNone);
var pictureBox = new PictureBox();
pictureBox.Location = panel.Location;
pictureBox.SizeMode = PictureBoxSizeMode.AutoSize;
pictureBox.Image = bitmap;
Controls.Remove(panel);
Controls.Add(pictureBox);
Rotation angles other than 90-degree increments are also possible, if you draw the bitmap into another bitmap using GDI:
var bitmap2 = new Bitmap(bmp.Width + 75, bmp.Height + 100);
var graphics = Graphics.FromImage(bmp2);
graphics.TranslateTransform(bitmap2.Width / 2, bitmap2.Height / 2);
graphics.RotateTransform(-15f);
graphics.TranslateTransform(-bitmap.Width / 2, -bitmap.Height / 2);
graphics.DrawImageUnscaled(bitmap, Point.Empty);
graphics.Dispose();
The problem of course is that you're only displaying an image of your panel, and not the panel itself, so it's no longer possible to interact with the controls inside.
That could probably be done as well, but you would have to mess with window messages, which gets quite a bit more complicated. Depending on your needs you might also be able to get away with handling click and key events on the PictureBox, manipulating the controls in the panel, and then updating the image.