1
general::
Honest, genuine, as in You can trust Pat with the money; he's straight as an arrow. This simile alludes to the arrow's undeviating flight through the air. [Second half of 1900s]
American Heritage Idioms
2
general::
Phrase(s): *straight as an arrow
1. Cliché [of something] very straight. (*Also: as ~.) • The road to my house is as straight as an arrow, so it should be very easy to follow. 2. Cliché [of someone] honest or forthright. (Straight here means honest. *Also: as ~.) • Tom is straight as an arrow. I’d trust him with anything.
McGrawhill's American Idioms And Phrasal Verbs