No it is not circular reasoning. because are reason tells us by creation their is a God.
Psa 19:1 The heavens declare the glory of God; and the firmament sheweth his handywork
Rom 1:19 Because that which may be known of God is manifest in them; for God hath shewed it unto them. 20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse
So we can see by Creation, evidence for a Creator, He has given us his word that tells us about Him, and tells us where to find authority. It is found by the word of God.
So those who speak the words of God - prophets (prophets are those who speak for God, not fore-tellers of the future as some define them)
So their was prophets given through out time to relay the word of God. In the days of the church, there were prophecies, special knowledge, and other gifts for understanding his will "TILL we all come to the unity of the faith" - i.e. The bible. I Cor 13:10 tells us these gifts would cease with that which is perfect comes, well if we look to see what "That (neuter form, not masculine, cannot be Christ)which is perfect" we see it is the word of God = Col 1:28, II Tim 3:15, Eph 4:13.
So we see also from Hebrews 1:1, Prophets are what God used "in times past" to relay his message but now speaks to us through Christ his son.
So to take the evidence of creation, and to examine a book that tells us were the authority lies in itself, is not circular reasoning. It no different than reading the constitution, believing it to be valid, and reading how itself has the authority over men, even though the men who wrote it are dead, it tells us itself, it should not be changed and is a crime to do so (even though many are doing it anyway).
We have a country - America, we see it's existence, we have a document, that is supposed to rule it, we read it, and accept it as the authority. We have a people Christians, a church made up of Christians, and a written document we accept as the authority of the church, because it says it is and there is evidence as to why it is to be the authority.
If no Bible, and still prophets, then the authority would lie with them, but the authority is the word of God, in whatever form it's in. Since the word of God explains how it came into being, (by the HS filling men so they could remember everything Jesus said and did, and write it later Jn 14-16) we accept that as truth.