The New 52 brought back Barbara Gordon’s original identity as Batgirl. It acknowledged her period crippled by the Joker through The Killing Joke but never specified whether or not she was ever Oracle as far as I know.
The Rebirth series Batgirl and the Birds of Prey answers that question in its first volume, subtitled Who Is Oracle?
The short answer is, yes, Barbara Gordon was Oracle for a period, but quit and went back to being Batgirl when she regained the use of her legs. This series opens with Barbara’s discovery that someone is using her Oracle name to sell secrets to the mob. That will require back-up from her former Birds of Prey partner Black Canary, and the pair also soon team-up with a new, more lethal heroine in the form of the Rebirth Huntress. All three are actually on the trail of the same master criminal, a new mob boss working to eliminate a number of her main competition and has a few snake-themed metahumans on her payroll. Barbara has to decide which identity she works best as: herself, Batgirl, or Oracle, while Huntress has to decide if she wants to be a solo act or part of a team.
Writers Julie and Shawna Benson do OK with the character dynamics, and artists Claire Roe and Roge Antonio aren’t bad (Roe is much better for what it is worth), but this new series doesn’t quite hold up to either Chuck Dixon’s original run or Gail Simone’s own superior one. Heck, I don’t recall the women ever referring to themselves as the “Birds of Prey” out loud like they do here. But as good as the character dynamics are, with Black Canary as something of a smart ass, experienced member, Batgirl as the uncertain leader, and Huntress as a far too serious woman with a penchant for violence, the fight sequences don’t work so well, nor does the pacing in places. The final battle in the last chapter reprinted here is especially problematic to follow. I’ve seen worse series, but this one didn’t grab me well enough to want to read any more. Seven out of ten moments where you wonder how good a cop Jim Gordon actually is. There’s probably room to grow here, but I don’t know that I am interested enough to find out.