The brass monkey is a cocktail consisting of equal parts:
The drink is thus basically a screwdriver cocktail with rum added.

Pulp free orange juice is usually desirable for reasons of palatability, though freshly squeezed juice may also yield a good brass monkey. Dark rum is also preferable, since it is the mixing of the brown rum with the orange orange juice that produces the distinct brass-like coloration for which this drink is named. It also tastes better.

Much of this drink's notoriety comes from the Beastie Boys' 1986 record "Licensed to Ill", which featured a track titled "Brass Monkey", which says:

"Monkey tastes Def when you pour it on ice
Come on y'all it's time to get nice"