Green’s Dictionary of Slang

rap n.2

[Ger. penny engraved with an eagle that had been drawn so crudely that it was known as a Rabe, a raven. The coin was presumably introduced to Ireland by Ger. mercenaries]

1. [mid-18C–1900s] a halfpenny; thus in US a cent.

2. [late 18C–early 19C] (orig. Irish) a counterfeit halfpenny, circulated 1700–50.

3. [late 19C] money in general.

In derivatives

rapless (adj.)

[late 19C–1900s] penniless.

In phrases

not care a rap (for) (v.) (also not give a rap (for))

[mid-19C+] to not care at all.

not matter a rap (v.)

[late 19C+] not to matter whatsoever.

not worth a rap

[19C–1900s] worthless, useless.