Is there a feat that changes your base attack to the number of hit dice you have?
No, there is no feat that changes your base attack at all.
The question sort of answers itself really. What would be the point of base attack if anyone could use a single feat to have the same as the fighters?
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There are feats that allow you to use your total hit dice in place of your BAB for certain things. For example, Defensive Combat Training allows you to use your hit dice instead of your BAB for computing your Combat Maneuver Defense.