Peter’s words in 1 Peter 2:23 are not a direct quote from Isaiah 53:1–12 (or anywhere else), but instead echo various emphases found in Isaiah 53:6–8. The reason an echo is sufficient (as opposed to a quote) is that Peter is not seeking to substantiate a dogmatic point through using an Old Testament prooftext but is seeking to draw out the significance of prophecy for contemporary conduct (1 Peter 1:10–11).
23 When he was reviled, he did not revile in return; when he suffered, he did not threaten, but continued entrusting himself to him who judges justly.