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).
And he shall cleanse the house with the blood of the bird, and with the running water, and with the living bird, and with the cedar wood, and with the hyssop, and with the scarlet:Leviticus 14:52 KJV