Not a single river but we can say single water body i.e. Parting of the Waters.
There's a natural spring in Yellowstone National Park in Wyoming that flows in 2 directions. One ultimately connects to the Mississippi River, which flows into the Gulf of Mexico. The other connects to the Columbia River, which flows into the Pacific Ocean. It's a natural wonder called the Parting of the Waters.
![enter image description here](http://uploads.neatorama.com/images/posts/366/71/71366/**********-0.jpg)