Green’s Dictionary of Slang

1. (US) an honest, clean-living, clean-cut, upright, if naïve and unsophisticated person.

1958		R. Frede Entry E (1961) 88: ‘Goddam, straight arrow,’ Trent said.
1968		Army Times ‘Army Talk in Vietnam’ 10 Apr. n.p.: straight arrow: serviceman who remains faithful to his wife or Stateside girl friend throughout his Vietnam tour.
1977		C. McFadden Serial 95: I’m really a straight arrow.
1990		(con. early 1950s) J. Ellroy L.A. Confidential 9: Ed Exley, the assistant watch commander, was a straight arrow.
2004		T. Winton ‘Fog’ in Turning (2005) 236: He wondered if it was his reputation as a bit of a straight arrow.
2010		(con. 1973) C. Stella Johnny Porno 23: ‘He ever connected?’ [...] ‘Please. John’s a straight arrow’.

2. (US gay) a heterosexual male.

1972

B. Rodgers Queens’ Vernacular.