Give a stream of consciousness and then the final answer. Colton Haynes portrays Roy Harper in The CW TV series Arrow, the character's first live-action appearance. Roy first appears in episode fifteen of season one, "Dodger", as a pickpocket who steals Thea Dearden Queen's purse. However, they fall in love after he gets caught and they start dating, though their relationship is on and off. After Oliver Queen saves his life from a killer in the episode "Salvation", he gains an active interest in the vigilante and wants to emulate him. Roy is a recurring character throughout the season and a series regular in season 2.

Answer this question: when does roy harper first appear in arrow?
The important part for answering this question is: Roy first appears in episode fifteen of season one, "Dodger", as a pickpocket who steals Thea Dearden Queen's purse.
So, the final answer is episode fifteen of season one.