"a rocking chair," 1852, American English, from rock (v.1); earlier "nurse charged with rocking a cradle" (early 14c.). In sense of "one of the curved pieces of wood that makes a chair or cradle rock" it dates from 1787. Slang off (one's) rocker "crazy" first recorded 1897. Meaning "one who enjoys rock music" (as opposed to mod (n.1)) is recorded from 1963, from rock (v.2).
Crazy; deluded; meshuga, nuts: I've been as near off my noodle as a sane man can get/ I suppose he was off his rocker (entry form 1945+, onion 1890+, rocker 1897+)