When we were facing some grave medical concerns over our youngest child, I would often go into the sanctuary of the church I served. I'd get there early and pray and sing hymns. I came to love the hymn, Lord, Thee I Love With All My Heart. Now, when I wake up in the middle of the night I'll sing the Agnus Dei or Kyrie (in my heart-not outloud!). I'll silently pray the Lord's Prayer, and recite psalms in those quiet hours. These calm my heart and God grants peace in those moments.
You may or may not have a great singing voice. But I'm confident that God loves to hear the songs we sing from our hearts and to his glory - no matter how well we may sing them.