Lay the rug flat on a clean outdoor surface and use a squeegee to squeeze out excess moisture. Push the squeegee in the direction of the fabric. If you don't have a squeegee or the appropriate outdoor surface, use a wet vac to suck out as much moisture as possible.
Roll the rug up into a cylinder and stand it up vertically until water stops dripping out.
Lay the rug outside on a clean area or hang it on a clothesline in the sun to dry. If weather conditions make this impossible, elevate the rug flat indoors and point an oscillating fan in the rug's direction to speed up the drying process. Once the rug is completely dry, the warping should disappear.