The Constitution specifies no details for the oath of office for Congress:
Constitution, Article 6 - Debts, Supremacy, Oaths
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
The first Congress developed this requirement into a simple, 14-word oath:
"I do solemnly swear (or affirm) that I will support the Constitution of the United States."
The Civil War led President Lincoln to develop an expanded oath for all federal civilian employees (April 1861). That July, when Congress reconvened, "members echoed the president's action by enacting legislation requiring employees to take the expanded oath in support of the Union. This oath is the earliest direct predecessor of the modern oath." (cite)
The current oath was enacted in 1884:
I do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter: So help me God.
The public swearing-in ceremony consists of Representatives raising their right hands and repeating the oath of office. This ceremony is led by the Speaker of the House, and no religious texts are used. Some members of Congress later hold separate private ceremonies for photo ops.
The Oaths Of Office