NB: This question was posed to me by an acquaintance. Let me state at the outset that I am answering this question as a biblical scholar and not in terms of the current policital climate in the US. In otherwords, my answer would not change regardless of who the current president is, nor what country I were writing about.
First, if one defines an “instrument of righteousness” in terms of a leader of a nation who is upholding the laws of the land in accord with his God-given responsibility, then it is easy to find some laws that even the most ruthless of leaders upholds and, thereby, conclude that that leader is such an instrument. In other words, almost anyone could argue that almost any leader is an “instrument of righteousness” based on this definition. This is a classic example of Edward Sapir and Benjamin Whorff’s principle “words create worlds”—which stated succinctly means that what people look for is what they find.
The primary problem, and there are many, with the suggestion the our current president is “an instrument of righteousness” is that it misunderstands what “righteousness” is. “Righteousness,” biblically defined, is not a moral category, even though that is how we tend to use it, but is always closely related to the covenant: see the phrase, “righteousness of God” throughout the books of Romans and Galatians. In these books, the phrase is intimately tied to God’s covenantal faithfulness.
Consequently, an OT king could be such an instrument if he upheld the law of God (God’s covenant) for the nation of Israel—note the connection with the people of God. In the New Testament, however, the covenant with Israel finds its fulfillment in Jesus; who begins “a new covenant.” To be an “instrument of righteousness” in the NT, then, means that one is advancing the new covenant; which Jesus proclaimed is the Kingdom of God.
[Thus, citing OT passages about God using kings to advance His kingdom is not applicable in the NT. Citing Romans 13 doesn’t work either because all Paul is saying there is that those in authority are meant to do right. That is, they are to maintain justice in the world. But this is different than bringing in the justice of the Kingdom of God; that is, national justice is not equal to justice done by the people of God—at least it cannot be now that the people of God are not a distinct national people group]
The key distinction between the old covenant and the new is that in the new covenant the people of God are no longer limited to a national identity. Instead, the people of God are composed of anyone who acknowledges that Jesus is Lord. If, then, an “instrument of righteousness” is one who advances the kingdom of God, then no secular leader can do so today (unless one were to suppose that God were to bring a nation-state against the church in judgment; but there is no NT indication that such will occur).
There are two kingdoms in the world today: the Kingdom of God and the kingdoms of the world. The Kingdom of God comes through faithful, persevering, sacrificial, and loving witness of God’s people. It stands opposed to the kingdoms of the world in that we proclaim Jesus is Lord while they proclaim Caesar is Lord.
A secondary problem arises with this presumption. Namely, in the present Christians are to be “instruments of righteousness” by advancing the Kingdom of God in both word and deed to the nations. When Christians take a stand politically and endorse people or laws it is imperative that we ask ourselves how will this affect my witness?