1
general::
Become a law-abiding person; abandon crime. For example, Once he got out on probation, he swore he would go straight. The use of straight in the sense of "honest" dates from the 1500s and probably alludes to the opposite of crooked, used in the sense of "dishonest" from the 13th century on.
American Heritage Idioms
2
general::
Phrase(s): go straight
to stop breaking the law and lead a lawful life instead. • The judge encouraged the thief to go straight. • After Bob was arrested, he promised his mother he would go straight.
McGrawhill's American Idioms And Phrasal Verbs