Certainly it is correct to say: Conscience is the voice of God.
From Notebooks 1914-1916, page 75, as translated by Gertrude Elizabeth Margaret Anscombe, first edition (1961), Second edition (1984).
This is the law of him in whom is the plague of leprosy, whose hand is not able to get that which pertaineth to his cleansing.Leviticus 14:32 KJV