The speaker, Stephen, is most specifically alluding to Exodus 19:3, where
Moses went up to God, and the Lord called to him from the mountain, saying, "Thus you shall say to the house of Jacob, and tell the children of Israel."
See also Psalm 147:19, where the psalmist avers that God "declares His word to Jacob, His statutes and His judgments to Israel."
The living oracles in Acts refers specifically to the Ten Commandments, more broadly to the Torah, which were to be given "to us," to the church of God. God's Old Testament utterances are for us today.
The Oracles of God
Multitudes of organizations in the Protestant world have no idea of what the church actually consists. This illustrates that even on the simplest of levels, the Bible is a "coded" book. Many refer to a physical building or a legal corporate structure as the church. Few seem to understand the church consists of the members themselves. The word "church" is translated from the Greek ekklesia, meaning "called-out" or "assembly." The "church in the wilderness" consisted of those called out of physical Egypt; the New Testament church are those called out of the spiritual Egypt of false belief and practice dominating this world. Without this knowledge, it is extremely difficult to identify the church Christ built.
Biblical Symbolism: Symbols of the Church
Other Forerunner Commentary entries containing Acts 7:38: