Your only real solution would be to drill a pass-through hole beside the door frame.
If you compress, crush, kink, twist, stretch, knot, or otherwise deform the jacketing on a Category-rated cable, it is likely to be out-of-spec, and your performance is likely to drop.
UTP is not designed to be walked or rolled on, it's a "bad thing."
If you go under a carpet with it, it should be contained in some crush-proof tube. It should not be stapled with regular staples (use wire clips). The minimum bend radius is ~two inches....so no sharp 90 degree bends.
Good Luck
Scott