According to Luke (Luke 23:26, Luke 23:33), Jesus was crucified on a cross. This cross would have been made from wood. Peter is referring to the fact that Jesus was hung up publicly on a piece of wood. Even if it was not a living tree, it is close enough to the same. The hanging of Jesus on a tree/wooden cross alludes to Deuteronomy 21:22–23,1 and is a confirmation that he was under the curse of God (see Galatians 3:13).
39 And we are witnesses of all that he did both in the country of the Jews and in Jerusalem. They put him to death by hanging him on a tree,