Arrow stealing is the act of taking arrows left on the ground by a ranger who will usually retrieve them at the end of their kill. It is not against the rules, but collecting arrows that another player is using is a contentious issue.
Some players consider arrow stealers to be unethical. Other players consider that when the arrows have been left long enough to be visible, they are "fair game" for anyone to take. Some players prefer to remain in a safe spot to range and do not intend retrieving their arrows.
The risk of losing arrows to arrow stealers is greater when attacking monsters of much higher level from a safe spot, as a combat can take so long that the first arrows fired are visible to other players before the combat is complete. In a PvP fight, F2P rangers may not pick up their arrows in time before someone else sees it and picks it up first.
The number of arrow stealers on F2P high-risk wilderness worlds (or previously bounty worlds) can get out of hand. The majority of rangers on F2P worlds use adamant arrows for PvP, and the ground is constantly scattered with piles of 1, 2 or 3 of them. Arrow stealers walk around collecting these, and hope for a pile of over 5 or so to appear. Since each arrow is worth 200 coins, a stack of 100 would fetch 20k.
This is only an issue in Free-to-play, because most members use Ava's accumulator to automatically retrieve arrows. Free players, however, do not have access to it and so they will always lose an arrow each attack.
If training in a populated area with the ranging skill, it is wise to bring arrows of a cheaper price in case an arrow thief makes his claim there.
Jagex's stand on this issue is as follows:
If someone picks up my arrows is that scamming?
No, if someone picks up an item that you have dropped because you no longer require the item then this is not item scamming. When you drop an item it takes a short length of time until it becomes visible to other players, so even if you drop the item accidentally you can still retrieve it again before anyone else has the chance to pick it up.
You may not drop items with the intention of trading them to another of your characters. This type of drop-trading is against Rule 8 in the rules of conduct.
In January 2007, Jagex released an update to the Animal Magnetism quest rewards: Ava's attractor or Ava's accumulator "will collect most of your own arrows as you fire them, saving you from having to pick them up." This only works if the safespot is one that has no obstruction, and if no metal armour is interfering with the magnetism.