Curling occurs because the corners of the rug are thinner than the rest of the rug.
One common cause of curling is exposure to heat. If the rug is located with extra heat, it’s best to remove it from the heat to let it uncurl. Move the rug into a cooler room or remove it from direct sunlight.
You can also spray a little bit of water on the rug and brush it until it regains its flat shape. Then add some weight to the corners for a day or two until it rests flat on its own.
Cowhide rugs can get severely damaged from exposure to water. It’s best to should never get it wet.