Green’s Dictionary of Slang

moisten v.

(US) to have a drink.

1882

A. Trumble Mysteries of N.Y. 15: The drivers, when not moistening in some convenient hostelry, loll on their boxes [...] hailing passers-by.

moisten one’s chaffer (v.)

moisten one’s wick (v.)

see under wick n.¹

moisten the clay (v.)

see under clay n.