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c.1300 "subject to light washing; wash with water only" (mid-13c. in surname Rinsfet), from Old French reincier (transitive) "to wash, cleanse" (12c., Modern French rincer), probably dissimilated from recincier, from Vulgar Latin *recentiare "to make fresh, to wash, cleanse with water," from Late Latin recentare "to make fresh," from Latin recens "new, fresh" (see recent). OED says similarity in form and sense with Old Norse hreinsa is "prob[ably] accidental." Meaning "wash a second time to remove remaining impurities, soap, etc." is from 1520s. Related: Rinsed; rinsing.
1837, from rinse (v.). As a hair treatment, by 1928.