From the Oxford English Dictionary
"Jones...2. slang. A drug addict's habit. 1968 Sun Mag. (Baltimore) 13 Oct. 19/4 Soon you're out to keep from getting the Jones. 1970 C. MAJOR Dict. Afro-Amer. Slang 71 Jones, a fixation; drug habit; compulsive attachment."
No one seems to have a theory on the origin of the word, but it appears to have appeared quite recently in its current meaning, say about 1965.