I'm in GA, no, not in our climate zone it is not required.
If you have housewrap under your siding, you already have a Class III vapor retarder installed in the optimum location - outside of the exterior wall.

The correct term is vapor retarder, a vapor barrier is specifically a Class I vapor retarder which blocks nearly all water vapor. You should ignore all posts which mention 'vapor barrier' instead of 'vapor retarder'. There are only a couple of posts which correctly use the term 'retarder'

In AL you can use rockwool, unfaced fiberglass, or kraft faced fiberglass with kraft paper facing exterior.

Adding a vapor retarder is not a fix for leaking/torn/improperly installed homewrap.