Traditionally, the prayers used for the Advent wreath for each week of Advent are the collects, or short prayers at the beginning of Mass, for the Sunday of Advent that begins that week. The text given here is of the collect for the Third Sunday of Advent (Gaudete Sunday) from the Traditional Latin Mass; you could also use the Opening Prayer for the Third Sunday of Advent from the current missal.
As we begin the third week of Advent, we anticipate Christmas, and so we ask Christ to grant us His grace that we might be prepared for welcoming His Birth.
Advent Wreath Prayer for the Third Week of Advent
Incline Thine ear to our prayers, O Lord, we beseech Thee; and make bright the darkness of our minds by the grace of Thy visitation. Who livest and reignest, with God the Father, in the unity of the Holy Ghost, God, world without end. Amen.