1610s, "band of leather," from Scottish and/or nautical variant of strope "loop or strap on a harness" (mid-14c.), probably from Old French estrop "strap," from Latin stroppus "strap, band," perhaps via Etruscan, ultimately from Greek strophos "twisted band; a cord, rope," from strephein "to turn" (see strophe). Old English stropp, Dutch strop "halter" also are borrowed from Latin, and the Old English word might be the source of the modern one. Slang meaning "credit" is from 1828.

"to fasten or secure with a strap," 1711, from strap, n.. Slang adjective strapped "short of money" is from 1857, from strap (n.) in the old sense of "financial credit" (1828). Meaning "to beat with a strap" is from 1735. Related: Strapped; strapping.