In both the manga and the anime, Rei practices the Shinto religion.. Rei is a miko. In the Shinto religion, a miko is a priestess sevring as an assistant at a shrine. Their roles include during ceremonial dances and assisting priests in wedding ceremonies. During ancient times, women who went into trances and spoke the words of a god were called miko.
Shinto means the way of the gods. As a religion, it's not based on a founder of sacred scripture, but living according to custom and the living and cating according to the guidance of the gods.
The anit-evil paper scrolls Rei uses are called ofuda. Ofudas are tablets or amulets on which the name of a deity(god) is written. They are considered to be symbols of the deity and can be made of wood or paper. They can be worshiped to obtain divine aid