Unfortunatelly, a soundtrack was never released but here's the title song sung by Sally Yeh:
(Save As...)
http://hkpmc.free.fr/mp3/the_killer.mp3
Several music cues are taken from other films, most notably Red Heat, and Hero and the Terror. The songs:
"Russian Streets" Composer: James Horner From: Red Heat (1988)
"Victor Escapes" Composer: James Horner From: Red Heat (1988)
"Bus Station" Composer: James Horner From: Red Heat (1988)
"Breakout" Composer: David Michael Frank (credited as David Frank) From: Hero and the Terror (1988)
http://en.wikipedia.org/wiki/The_Killer_%28film%29#Music_Cues