Is there a feat that's the opposite of the Combat Expertise feat? I'm looking for a feat which would allow you to subtract a number from your AC and add it to your attack roll.
It's not really a feat but more of an action you can choose in combat. If you use the charge attack and move at least 10ft and have an unobstructed path to your target you can move up to double your movement speed and make a single attack that gains +2 to the attack roll but suffer -2 to AC until your next turn. I used to do that with my half orc barbarian to guarantee a hit on the first attack.
As @KRyan says, there is no such feat. However, what you're looking for does exist in a class feature. 3 levels of War Chanter allow you to use Bardic Music to Inspire Recklessness in yourself and your allies, letting you (and them) take a penalty to AC up to your BAB and add it to your attack bonus.
You may also be interested in the Shock Trooper feat, which (among other things) lets you take your Power Attack penalty from AC instead of BAB when charging, allowing you to sacrifice your AC for damage.
No such feat exists. If it did, nearly everyone (who wants to make attacks, that is) would take it, because it would be amazing. You would see it recommended constantly, listed in every martial-class handbook, and so on, but you do not.
Combat Expertise is a really poor feat—even if you have it, most of the time it is the wrong choice to activate it. Quite simply, AC is a weak defense—most characters rely on non-AC defenses rather than waste the money it costs to keep AC relevant at mid-to-high levels. Meanwhile, attack bonus allows you to kill things, which is the greatest defense in the game—things cannot hurt you once they are dead. The only reason Combat Expertise gets taken at all is because of the feats that require it—and even once you have it, it’s rarely a good choice to use it.
Therefore, “flipping” Combat Expertise is not balanced—inverting an unreasonably bad trade becomes an unreasonably good one.
There is a Reckless Offense feat that adds +2 to all attack rolls at the expense of a penalty of -4 to your Armor Class. The exchange is active until your next turn.
The feat is from the psionic feats list but it is a general feat that requires only +1 base attack bonus.
Thank you everyone. I found what I was looking for. It's in a 3rd party publication called Quintessential Fighter.
To be more precise, it's called Reckless Attack (not to be confused with Reckless Offense which is similar but different), it's found on page 39, and it actually adds to damage not attack.
However, when combined with Power Attack, Combat Expertise, and Unerring Strike (Kingdoms of Kalamar Players Guide p. 92), you can shift your bonus between AC, Attack, and Damage allowing you supreme flexibility.
Unerring Strike let's you take a number from Damage and add it to Attack.