Rite

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Middle English: from Latin ritus ‘(religious) usage’.

wiktionary

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Via Middle English and Old French, from Latin ritus.

Variation of right.

etymonline

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rite (n.)

early 14c., "formal act or procedure of religious observance performed according to an established manner," from Latin ritus "custom, usage," especially "a religious observance or ceremony" (source also of Spanish, Italian rito), which perhaps is from PIE root *re- "to reason, count," on the notion of "to count; to observe carefully." Rite of passage (1909), marking the end of one phase and the start of another in an individual life, is translated from French rite de passage, coined by French anthropologist Arnold van Gennep (1873-1957).