OK... you are mixing up apples & oranges ...
First to make a contribution you must have earned income. Not sure what the $12K AGI you mentioned is comprised of.
Next, if you qualify to make a ROTH contribution you cannot deduct it on the return. It cannot reduce your AGI.
And lastly ... if your income is low enough that the standard/itemized deduction & personal exemptions zeros out your income then you will pay no federal taxes.
