There is a barbarian rogue in PFS who has questioned several GMs in Society and has gotten mixed answers about this. The rules don't say he can't. Some GMs say yes, others say No. The argument against is that it requires clarity of thought to perform precision damage.
The argument for, is that performing a sneak attack is not a full round action and how many rogues put points in things like "knowledge anatomy". Really, any idiot could find "where it hurts most". If the barbarian doesnt have an intelligence penalty... He should be able to stab you in the face.
The following is copied from the "Rage" section on the Barbarian page on Paizo's PRD:
"Rage (Ex): A barbarian can call upon inner reserves of strength and ferocity, granting her additional combat prowess. Starting at 1st level, a barbarian can rage for a number of rounds per day equal to 4 + her Constitution modifier. At each level after 1st, she can rage for 2 additional rounds. Temporary increases to Constitution, such as those gained from rage and spells like bear's endurance, do not increase the total number of rounds that a barbarian can rage per day. A barbarian can enter rage as a free action. The total number of rounds of rage per day is renewed after resting for 8 hours, although these hours do not need to be consecutive.
While in rage, a barbarian gains a +4 morale bonus to her Strength and Constitution, as well as a +2 morale bonus on Will saves. In addition, she takes a –2 penalty to Armor Class. The increase to Constitution grants the barbarian 2 hit points per Hit Dice, but these disappear when the rage ends and are not lost first like temporary hit points. While in rage, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except Acrobatics, Fly, Intimidate, and Ride) or any ability that requires patience or concentration.
A barbarian can end her rage as a free action and is fatigued after rage for a number of rounds equal to 2 times the number of rounds spent in the rage. A barbarian cannot enter a new rage while fatigued or exhausted but can otherwise enter rage multiple times during a single encounter or combat. If a barbarian falls unconscious, her rage immediately ends, placing her in peril of death."
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The following is copied from the "Sneak Attack" section on the Rogue page on Paizo's PRD:
Sneak Attack: If a rogue can catch an opponent when he is unable to defend himself effectively from her attack, she can strike a vital spot for extra damage.
The rogue's attack deals extra damage anytime her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target. This extra damage is 1d6 at 1st level, and increases by 1d6 every two rogue levels thereafter. Should the rogue score a critical hit with a sneak attack, this extra damage is not multiplied. Ranged attacks can count as sneak attacks only if the target is within 30 feet.
With a weapon that deals nonlethal damage (like a sap, whip, or an unarmed strike), a rogue can make a sneak attack that deals nonlethal damage instead of lethal damage. She cannot use a weapon that deals lethal damage to deal nonlethal damage in a sneak attack, not even with the usual –4 penalty.
The rogue must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. A rogue cannot sneak attack while striking a creature with concealment.
