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.