In the Hail Mary, we regularly address the "Mother of God." Mary gained this title by being the Theotokus — literally, "God bearer."
The title "Mother of God" does not divinize Mary, but draws attention to the dual nature of Christ — truly God and truly human. The title also reminds us of her special role in bringing Christ to the world.
Mary was petitioned as "Mother of God" at least by the 3rd Century, as is evidenced by the discovery of the Sub Tuum prayer:
We fly to your protection O holy Mother of God, despise not our petitions in our necessities but deliver us from all dangers, ever glorious and blessed Virgin.