There's not a shred of Scriptural support for that.
Show us where in Scripture there are instructions about Peter's successor, how he was to be picked. Where did Peter leave any instructions about the matter?
Go tell that to the litany of theological giants and the early Church Fathers. There was about 30-40 years of oral tradition before Scripture was written and it is the Catholic Church that authoritatively selected the books we call the Bible. These books did not fall from the sky! Christ sent His disciples and founded His Church to present ONE truth for all time to come.