Green’s Dictionary of Slang

(US drugs) to tie a rubber tube or similar ligature around the arm in order to make a vein prominent prior to injecting a narcotic.

1955		‘Hal Ellson’ ‘I Didn’t See a Thing’ in Tell Them Nothing (1956) 143: Bug-Eye ties up their arms, takes a spoon, puts something in it.
1969		‘Iceberg Slim’ Pimp 95: My eyes begged him to tie me up and bang me.
1978		H. Selby Jr Requiem for a Dream (1987) 55: She was alert enough to tie up and pump up a good vein.
1989		(con. 1939) Courtwright & Des Jarlais Addicts Who Survived 114: They let me tie up and get off in front of them.
1992		R. Price Clockers 437: We see the three guys that beat us sitting on the floor with their works, tying up and shit.
2001		(con. 1964–8) J. Ellroy Cold Six Thousand 154: They fed the spike. They tied up. They geezed. They dipped. They nodded.