1580s (intransitive), perhaps a nasalized variant of scrabble (v.), in its sense of "to struggle, to scrape quickly." Transitive sense "to stir or toss together randomly" is from 1822. Broadcasting sense "to make unintelligible" is attested from 1927. Related: Scrambled; scrambling. Scrambled eggs first recorded 1843.
1670s, "an eager, rude contest or struggle," from scramble (v.). Meaning "a walk or ramble involving clambering and struggling with obstacles" is from 1755. Meaning "rapid take-off" first recorded 1940, R.A.F. slang.