I am a great prayer of exultant praise,
Prayed each evening at the ends of days.
Sung first by a young woman, Mary by name,
Just newly pregnant, to her cousin she came.
She sings of God’s care for the poor and the lowly.
She rejoices in wonder of our God so holy.
What am I?

The answer: Mary’s Song of Praise, also known as "the Magnificat"!
The Magnificat (called that because Mary says “My soul magnifies the Lord” - what can she mean? How does a soul make the Lord magnified?)
is said daily by Catholics who pray Evening Prayer, and has been set to music many times. Two of my favourite settings:
https://www.youtube.com/watch?v=1ewLM2N9lDM
https://www.youtube.com/watch?v=QAy08-WkeqU