With the introduction of the Faithful Cartographer update in The Long Dark, players are now able to kill Rabbits with stones. Well, they can stun Rabbits with stones, but must do the killing part themselves, which is not for the faint of heart.
How to Kill Rabbits with Stones

The first step of the process is to find a Stone, which isn’t very hard. You should be looking at the ground to pick up Sticks most of the time anyway, so now you just add Stones to your shopping list.
The next step is to find a Rabbit which, if you’re a veteran player, you should be able to do by now. If you’re new to the game, you can use Whiteberry’s maps to find Rabbit spawns, or you can create your own in-game maps through the Navigation feature.

When you’re close to a Rabbit, crouch down and equip the Stone the same way that you would equip any other weapon. Use your right mouse button to aim, trying to use your character’s left hand as a guide. When the Rabbit is within a few feet, throw the Stone.

Hitting the Rabbit will briefly stun it, at which point you must quickly approach the animal and pick it up. If you’re too slow, The Rabbit will run off and you’ll have to try again. However, if you reach your prey before it comes to, you can pick it up using the left mouse button, and kill it by snapping its neck. This will place the Rabbit in your inventory, allowing you to take it inside where it’s warm to harvest.
Killing Rabbits with Stones is fun and all, but the biggest threat in The Long Dark is the cold, which is why we put together a complete clothing guide.