A person who drinks alcohol is called a drinker.
Example sentences:
He's a heavy drinker. He drinks every day.
She's not a drinker. She only has a drink or two at social events.
Alternatively, you could use the term "alcohopc" to describe someone who is dependent on alcohol and cannot control their drinking.
Example sentence:
He's an alcohopc. He needs help to stop drinking.