If you have freedom to move the rugs, the easiest solution could be to temporarily hang them from a wall and the simply photograph them straight on horizontally.
If the rugs must be photographed in place, one cheap and easy solution would be to stand on a ladder along the middle of one edge of the rug, pointing the camera downward. This will of course result in converging lines, making the rug appear like a trapezoid. This can be corrected in post processing by using the perspective correction feature of software like Lightroom, typically used to correct the converging lines of the similar geometric situation of tilting a camera upward to photograph a building. You may be able to avoid the post processing step by resting a tilt-shift lens and using it to correct the converging lines in the camera.
The Gorillapod SLR-Zoom is a tripod with flexible legs that can be securely mounted anywhere it's legs can wrap around, so if the ceiling has anything in approximately the right location that a Gorillapod could attach to, this could be a relatively inexpensive solution for mounting the camera directly above the rug. Since the camera might be quite awkward to control in this location, it may be necessary to tether it to a computer with Canon's EOS Utility software.