A Rat's tail is a quest item used in the Witch's Potion miniquest. It can be obtained by killing any rat in RuneScape after the player has begun Witch's Potion. The item has a 100% chance to drop once you begin the miniquest.
Brian's Archery Supplies, a store that sells Ranged supplies, has a couple of rats which are very convenient for the player, since the store is located near Hetty the Witch's house.
After completion of the miniquest, the Rat's tail is unobtainable unless you are to kill a rat, complete the quest and pick it up. If the player shows a Rat's Tail to the Wise Old Man after completing the miniquest, he will tell the player to get rid of it. (Before completing he says "You have brought me a tail of a rat!" and "Yes, I think you should keep it for now.")