Is there any prayer or ceremony for becoming a Noahide?

There is no ceremony or specific prayer necessary. It only depends on your decision, by learning G-d’s commandments of the Noahide Code, and living in that righteous path.

Here is the explanation from Rambam (Maimonides), who was one of the greatest Torah Sages, about the meaning of a “righteous Gentile” [emphasis and text in brackets added for clarity]:

Any Gentile who accepts the seven commandments and is careful to observe them is of the “pious of the nations of the world” and will have a portion in the World to Come. This is so provided that one accepts them and observes them because the Holy One, blessed be He, commanded them in the Torah and informed us through Moses our teacher that the descendants of Noah were originally commanded about them.

But if one observes them only by virtue of common sense [separating them from their connection with G-d], he is not a “Ger Toshav” [a Hebrew Biblical term identified with one who takes on the Noahide Code], or one of the “pious of the nations of the world,” [in today’s language, an “observant Noahide”] but rather, [merely] one of their wise people.

[From Rambam, Laws of Kings 8:11. ]