1740, "acting by itself;" see self- + acting (adj.). The mechanical sense of "contrived for superseding manipulation in the management of a machine" is by 1844.
Entries linking to self-acting
self-
word forming element indicating "oneself," also "automatic," from Old English use of self (pron.) in compounds, such as selfbana "suicide," selflice "self-love, pride, vanity, egotism," selfwill "free will." Middle English had self-witte "one's own knowledge and intelligence" (early 15c.).
OED counts 13 such compounds in Old English. Middle English Compendium lists four, counting the self-will group as a whole. It re-emerges as a living word-forming element mid-16c., "probably to a great extent by imitation or reminiscence of Greek compounds in (auto-)," and formed a great many words in the pamphlet disputes of the 17c.
acting adj.
1590s, "putting forth activity, active," present-participle adjective from act (v.). Meaning "performing temporary duties" is from 1797.