From the Public Ledger, 11 May 1836, pg. 3, col. 1:

They play _Poker_. The two men above named were held in their own

recognizance of $100 to appear to-morrow morning at the officer, and a warrant

was issued for String; we have no doubt but that his Honor will _poke_ him

into jail.

OED's earlier "poker" (card game) is also 1836.