What is the simplest circuit to rotate TV Picture 90 degrees?
If you mechanically rotate the magnetic deflection yoke it will rotate the picture, but a lot of things will probably go pear-shaped.

Edit: The easiest way, in that case, would be to have a second TV and point a camera at it sideways or something along those lines.    . Anything else will be very complex. (In the olden days there were scan converter vacuum tubes that performed an analogous function).
For example, a computer with a video capture card that can output rotated VGA and a VGA to video converter.
It might also make a good project for a moderate size FPGA if you were willing to invest a lot of time into it.