Now Jesus did many other signs in the presence of the disciples, which are not written in this book. But these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in His name. John 20:30-31 ESV

God inspired the Gospel of John so that we would have the facts, believe, and thusly be reconciled in our relationship with Him. Let he who has ears to hear listen and understand.

So that is a subordinating conjunction that introduces a clause of purpose or result, often indicating an action taken with a specific goal in mind. This series explores the so that of the providence of God. See here.