There's nothing explicit in the rules about it. As @HeyICanChan points out, there's a long list of things that a raging barbarian can't do, and fighting defensively (or even using total defense) isn't on that list.

At the same time, the list of restrictions isn't exhaustive. One of the items on the list is "any abilities that require patience or concentration." It's a plausible thing to say that fighting defensively requires patience and concentration, and is thus restricted. Certainly you can argue from realism: if you're not carefully keeping track of incoming attacks and watching for openings to attack yourself, then you're not going to be very good at it.

But that is a ruling, not RAW. If you're comfortable with that, then that's fine: the reasoning is easy to follow. Just be aware that some DMs may see things differently.

Barbarian rage and fight on defense
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