I don't think it's possible through normal means. Every time I've had an item take on a bizarre angle of orientation when moving it around, it's always snapped back to its intended orientation when I try placing it.

Whether there's some mod out there can be used to accomplish it is something I don't know and don't care to investigate.

It really would be nice if SE would add the ability to rotate items around any axis in addition to giving us control over vertical placement without resorting to glitches.

If you're trying to get the look of an awning or very thin shelf, I'd probably go with floating a rug instead.