My AC duct coming out of the AC unit in the attic is soaked with water. It started to leak out and onto the sheet rock and is causing a leak in the ceiling. What is causing this?

Condensation is causing your problem. Most likely you have ducts that are not insulated and/or sealed correctly which is allowing warm humid attic air to come in contact with the cold duct. This will drop the temperature below the dew point and cause the condensation which then soaks the duct insulation and when that can't hold any more it starts to drip out at the low points which unfortunately is your ceiling.

It sounds like you have a system retrofitted into your house. In my opinion, attics are the worst places to run ducts and do a good install. Current home retrofits usually use duct board for the trunks and flex out to the grills. The transition is a metal collar which, if the flex isn't carefully installed, will be exposed to the ambient air and consequently cause condensation when in the cooling mode. This not only is bad for your ducts and house, but also your wallet. You are trying to air condition the attic.

You will have to inspect the ducts and find where the condensation is happening and then seal and insulate things until the condensation problem is cured. You might have to puncture the outer layer of the flex to let puddled water out so things can dry out or even replace sections of soaked duct and install it correctly. After fixing the water problem, you might have to cover the duct system in the attic with fiberglass batts to insulate it correctly so that you aren't losing so much energy to the attic. If the temperature at the supply grill fartherest from the AC unit is more than 3 to 5 degrees warmer than the supply closest to the unit, your ducts are NOT insulated correctly. Make certain you measure that on a good hot day. :)

Good luck