A piece of rope can be found in several locations. The most easily accessible piece is located on the floor just inside the Black Boar Inn in Broken Valley Village. Another can be found in Folo's house.
You can also create a rope from the console menu:
- give QI_Rope_A
- give QI_Rope_B
A rope is required for the Stuck in a Hole quest. This is hinted at in the item's description: "A long, solid, sturdy piece of rope. It could have many uses, like lifting someone up from a deep hole. Who would be clumsy enough to fall into a hole, though?"