The Reformed Presbyterian Church of North American in its Directory of Public Worship teaches about the principle of covenanting:
"Covenanting with God is a solemn act of worship in which individuals, churches, or nations declare their acceptance of Him as their God and pledge allegiance and obedience to Him. Public covenanting is an appropriate response to the Covenant of Grace. The 'Covenant of Communicant Membership' is to be accepted by individuals who profess faith in Christ and unite with the Church. Ordinarily, such individuals are to give public assent to this covenant in the presence of the congregation. When circumstances warrant, churches and nations also may produce statements of responsibility arising from the application of the Word of God to the times in which they are made. Such covenants have continuing validity in so far as they give true expression to the Word of God for the times and situations in which believers live. (For a fuller discussion of vows and covenanting see Testimony, chapter 22 ['Of Lawful Oaths and Vows'], especially paragraphs 8 and 9.) Examples of such covenants are the Scottish National Covenant of 1638, the Solemn League and Covenant of 1643, and the Reformed Presbyterian Church of North America’s Covenant of 1871."
On May 27, 1871, the Synod of the RPCNA, meeting in Pittsburgh, Pennsylvania, entered into a solemn covenant and confession of sins before the Lord. The history of this event as well as the text of the Covenant itself is recorded by William Melancthon Glasgow in his History of the Reformed Presbyterian Church of America. Glasgow notes concerning Samuel Oliver Wylie (1819-1883) that "He was the Chairman of the Committee which drafted the Covenant of 1871, and, with a few changes, was adopted as it came from his pen." The Covenant has six sections - section 5 is reproduced here. The history and full text of the 1871 Covenant (also known as the "Pittsburgh Covenant") from Glasgow can be read here.
"5. Rejoicing that the enthroned Mediator is not only King in Zion, but King over all the earth, and recognizing the obligation of His command to go into all the world and preach the gospel to every creature, and to teach all nations, baptizing them in the name of the Father, of the Son, and of the Holy Ghost, and resting with faith in the promise of His perpetual presence as the pledge of success, we hereby dedicate ourselves to the great work of making known God's light and salvation among the nations, and to this end will labor that the Church may be provided with an earnest, self-denying and able ministry. Profoundly conscious of past remissness and neglect, we will henceforth, by our prayers, pecuniary contributions and personal exertions, seek the revival of pure and undefiled religion, the conversion of Jews and Gentiles to Christ, that all men may be blessed in Him, and that all nations may call him blessed."
Of this section it has been noted: "We hail with delight one special feature of this Pittsburgh Covenant—its recognition of the obligations to missionary and evangelistic effort. There is particular allusion, it is true, to this duty in the Solemn League and Covenant, but it is entirely overlooked in subsequent renovations of it, or the Bonds of Adherence which the Churches, from time to time, have adopted. It is here brought out with a clearness and prominence worthy of its great importance. There is something touching in the express references to past shortcomings on this head. They furnish evidence that the men who framed and subscribed this Covenant are not moving in the mere groove of antiquated forms and traditions, but are alive and awake to the momentous responsibilities of the present hour" (The Reformed Presbyterian Magazine, Oct. 2, 1871).
The RPCNA entered into a briefer Covenant subsequently on July 18, 1954. But it was the Covenant of 1871 that signified a distinctly American application of the principle of covenanting within the RPCNA. Take time to read the six sections, and Glasgow's history of a special day in the history of Reformed Presbyterianism in America here.