Currently, you cannot feed Polar Bears in Minecraft. As a result, you cannot tame or breed them. Though, it is implied that they eat, just not anything given by you. This can be seen by noting their item drops.
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What Kind of Foods Do Polar Bears Like?
Despite being unable to feed a Polar Bear yourself, you may be able to do so in a future update. What food items this would involve can be speculated upon by looking at the items that Polar Bears drop when they are slain.
Items That Polar Bears Drop
When defeated, a Polar Bear has a 75% chance to drop up to 2 Raw Cod. Additionally, there is also a 75% chance for them to drop up to 2 Raw Salmon in the same way.
From this, it would make sense to assume that Raw Cod and Raw Salmon are what Polar Bears like to eat in Minecraft. And, if the ability to feed them yourself becomes possible in a future update, these are the items that you would likely use.
