Green’s Dictionary of Slang

tie-up n.4

[tie up v.4 ]

(drugs) the rubber tube, handkerchief, string or other object used for tying off a vein before injecting narcotics.

[US]‘William Lee’ Junkie (1966) 159: Tie Up . . . Tie, or handkerchief, used as a tourniquet for a vein shot.