"supply land with water," 1610s, from Latin irrigatus, past participle of irrigare "lead water to, refresh, irrigate, flood," from assimilated form of in- "into, in, on, upon" (from PIE root *en "in") + rigare "to water, to moisten," of uncertain origin. Perhaps [Watkins] from PIE *reg- (2) "moist" (see rain (n.)). De Vaan offers as possibilities the root of regere "to direct, lead," on the notion of leading water onto the fields, or to the root of rigere "be stiff," literally "stretch." The first better suits the sense, but has phonetic problems.
Related: Irrigated; irrigating. In Middle English it was an adjective, "watered, flooded" (mid-15c.). Other adjectival forms have been irriguous (1650s), irrigative (1842), irrigatorial (1867).