Green’s Dictionary of Slang

1. (orig. US black) talking.

1969		R.R. Lingeman Drugs from A to Z (1970) 219: rapping [...] (1) talking. (2) random free-form conversation.
1970		A. Young Snakes (1971) 106: ‘We might have to talk to those people.’ [...] ‘I aint about to waste my good high rappin with them stuck-up cute niggers.’.

2. (US black) a form of consciously stylised speech, usu. based on individual communication style.

1969		T. Kochman ‘“Rapping” in the Black Ghetto’Trans-action Feb. 27: While often used to mean ordinary conversation, rapping is distinctively a fluent and a lively way of talking, always characterized by a high degree of personal style.
1970		R.D. Abrahams Positively Black 155: In the uprisings on campus we witness an exhibition of soul-brothering in the deliberate use of street-style rapping [...] [...] It is ‘throwing a rap’ at the others, asking for a response in kind. It is process talk, in which someone ‘caps’ on another, ‘charging,’ ‘mounting,’ ‘running it out.’.