Old English spinnan (transitive) "draw out and twist fibers into thread," strong verb (past tense spann, past participle spunnen), from Proto-Germanic *spenwan (source also of Old Norse and Old Frisian spinna, Danish spinde, Dutch spinnen, Old High German spinnan, German spinnen, Gothic spinnan), from PIE *spen-wo-, suffixed form of root *(s)pen- "to draw, stretch, spin."
Intransitive senses of "to form threads from fibrous stuff; to twist, writhe" developed in late Old English. Transitive sense of "cause to turn rapidly" is from 1610s; intransitive meaning "revolve, turn around rapidly" first recorded 1660s. Meaning "attempt to influence reporters' minds after an event has taken place but before they have written about it" seems to have risen to popularity in the 1984 U.S. presidential campaign; as in spin doctor, first attested 1984.
1831, "a rapid revolving motion," from spin (v.). Meaning "fairly rapid ride" is from 1856. Sense of "a twisting delivery in throwing or striking a ball" is from 1851. Sense in physics is from 1926. Meaning "act of playing a phonograph record" is from 1977. Meaning "influence imparted by a media source" is from 1984.