The letter-winged kite was described by ornithologist John Gould in 1842 under its current binomial name Elanus scriptus. The specific epithet is from the Latin word scriptum, meaning "written" or "marked". British explorer Charles Sturt wrote of seeing them on his travels in his 1849 book Narrative of an Expedition into Central Australia. The letter-winged kite is monotypic: no subspecies are recognised, nor is there any recorded geographic variation. Molecular evidence shows that the letter-winged kite and its relatives belong to the subfamily Elaninae, an early offshoot within the raptor family Accipitridae. There is some evidence that they may be more divergent from other raptors and better placed in their own family.
"Letter-winged kite" has been designated the official English-language name by the International Ornithologists' Union (IOC), derived from the letter-like markings under the wings. In Central Australia, southwest of Alice Springs, the Pitjantjatjara name for the letter-winged kite is nyanyitjira. It has been incorrectly called white-breasted sparrowhawk.