No browser that I know of works this way. There isn't a way to force the screen orientation. The browser itself sets the screen orientation based on the actual device orientation, and then the webapp can determine what orientation the device is in and respond accordingly.
Some browsers have manual user controls to force orientation. For example, iOS has an "orientation lock". This is not exposed via Javascript, however. Perhaps some other devices have an exposed orientation control, you would have to investigate and implement on a case-by-case basis.
There is a hack you can use, but I don't think you'd be very happy with the result. You can use CSS transforms to rotate the page content. It's likely not pretty, though. Do some searches, and you will find some implementations of this.