Albert Barnes Commentary Psalms 109:27

"That they may know that this is thy hand; [That] thou, Jehovah, hast done it." — Psalms 109:27 (ASV)

That they may know that this is thy hand— That this has been done by you; that it has all occurred under your direction, or has been ordered by you. The reference seems to be particularly to God’s interposition: “Let it be manifest to all that you have interposed in my behalf; that you have undertaken for me; that you are my Friend.” He desired an interposition from God that he might be vindicated before all his enemies.

That thou, Lord, hast done it— Let it be such an interposition that it will be manifest to all that no other one but God could have done this.