You can't rotate a projected image with flat mirrors alone, only reverse it.
True, for rotation you need to use something like a Dove prism:
But as Joerg mentioned, the nearly square S8 frame turned sideways is hardly portrait. A fairly simple method to get a more vertical projection aspect ratio is to shoot and then project with a 2X anamorphic lens turned 90 degrees (so that it compresses and later uncompresses vertically). This is what Tacita Dean did for her marvellous Tate installation. A 4:3 horizontal frame would become a 4:6 vertical one, some masking of the sides could make it more portrait still.
Or simply mask a normal frame, but you'd lose a lot of image area.
For an installation that may be running for a while I don't think turning a projector sideways would be a good idea.