You find them at pregenerated NPC villages, they have small patches of farmland surrounded by wooden logs, you can harvest their carrots and potatoes so you can go grow your own.
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Just like in real life, you can't "make" carrots in Minecraft. You can, however, plant them just like seeds and potatoes.
You can mostly find carrots in a village or there dropped by zombies on rare occasions.
you get carrots in minecraft from baby zombies on chickens or spiders, you have to kill them and then you will get them.
Carrots.
Witches, bats, wither skeletons, the wither mob boss, heads, anvils, becons, carrots, potatoes, baked potatoes, golden carrot, carrot on a stick (leads a pig around when riding it), and pumpkin pie.