Green’s Dictionary of Slang

(US) a rustic, a peasant.

1900		E.H. Babbitt ‘College Words and Phrases’ in DN II:i 69: wheat, n. An unsophisticated fellow.
1908		T.A. Dorgan in Zwilling TAD Lex. (1993) 87: (This Is The Thaw Trial, Not The 6-Day Bike Race) Stack of wheats 2.