Rat's paper is a quest item used only during the quest What Lies Below. The player obtains the paper by killing outlaws in the camp west of Varrock and east of Edgeville. Once the player has obtained five papers they can be put in the empty folder given by Rat Burgiss to create a full folder.
When the player chooses the Read Rat's paper option, it reads: The piece of paper appears to contain lots of facts and figures. They look like accounts and lists of items. You're not sure what they all mean.
When handing in the full folder to Rat, any excess papers are also removed from the player's inventory.
For an exhaustive list of all known sources for this item, see here