While there is no mechanic to tame rabbits like there is with dogs, cats, and horses, there is still a way to keep them as pets. Keep plenty of carrots on hand when exploring biomes to bring one home.
Players can use carrots or a trail to get them to follow. Using a leash is the preferred method, as carrots require more attention and a slower movement. Rabbits can also become disinterested, and switching between food to eat and carrots to drive can be intimidating. Related: How To Make A Track In Minecraft (2021) Back Home, Players Can Make An Enclosure, A Hole, Or Keep Them In Their House With A Door. For enclosures, fences or walls will do as long as there are no blocks around the perimeter that can be used by rabbits to escape. Keeping them inside with a door is simple as the player only has to close the door to prevent them from going out. Holes in the ground can also be used and only need two blocks deep to keep them from jumping.
Once placed at home in a hole, fence, or house, rabbits can be raised among themselves. Using carrots or dandelions, rabbits will breed just like any other animal in the game. For more information on how to get even more pets, look at How to Tame an Axolotl in Minecraft on the Guides.