Does Origin have any built in screenshot functionality?
Origin does not support screenshots. You will have to use FRAPS or Steam to make them or the game's functionality if there is any.
What i have become accustomed to doing is having microsoft paint open when i play my games. When i do good in a match and im looking at the scoreboard i can just do a Print Screen and paste it into paint where i save it as an image. Its not very conveniant but hey, at least its something!