Green’s Dictionary of Slang

1. (drugs) for withdrawal symptoms to start affecting a narcotics addict.

1938

D. Maurer ‘Lang. of the Und. Narcotic Addict’ Pt 2 in Lang. Und. (1981) 102/1: To feel the habit coming on. See to be sick.

2. (drugs) for a drug to begin affecting its user, esp. of a hallucinogen (which takes a short time to enter the bloodstream and hit the brain).

1946		Mezzrow & Wolfe Really the Blues 92: Muta never came on like that.
1973		E. Bunker No Beast So Fierce 214: The marijuana came on quickly.
1985		(con. 1969–70) D. Bodey F.N.G. (1988) 103: Whatever that pill is, it’s coming on hard now.

3. of a woman, to start menstruating.

1982		P. Bailey Eng. Madam 45: I’d clicked with him once before, and he gave me some pills [...] and I came on again after taking them.
1999		K. Sampson Powder 130: All the girls had come on their period that night.
2001		OnLine Dict. of Playground Sl. 🌐 come on v. to begin menstruation.

4. (US) to join, to begin a job or career.

1991

B. McCarthy Vice Cop 69: Those two hooked up with another cop who had come on about the same time I did.