The exact wording may not be there, but for the last 2+ centuries, the phrase:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof

has been understood to mean just that - the government can not legalize religion. Most educated individuals consider this the basis of the American philosophy of Religious Freedom and the Separation of Church and State.

To institutionalize prayer in classrooms would need an act by the ELECTED (ergo, public) school board. If you want prayer in school, go to one run by your religion.

As Lady Macbeth said:
Do not stand upon the
order of your leaving,
just get the heck out of
here! (thanks RBG)