"aware of oneself," in a psychological sense, 1892, a back-formation from self-awareness, or else from self- + aware.
Entries linking to self-aware
self-awareness n.
"condition of being aware of oneself," 1876, from self- + awareness.
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.
aware adj.
Middle English aware, from late Old English gewær "watchful, vigilant," from Proto-Germanic *ga-waraz (source also of Old Saxon giwar, Middle Dutch gheware, Old High German giwar, German gewahr), from *ga-, intensive prefix, + *waraz "wary, cautious" (from PIE root *wer- (3) "perceive, watch out for").