According to a Microsoft store listing (via IGN), Arkham Knight will release on February 24, 2015. Retailers often put placeholder dates on games, but this one is a bit different. It's not at the beginning or end of a financial quarter, and on top of that, it falls on a Tuesday like most game releases.
The date isn't official, of course, so until Warner Bros itself confirms it, consider this firmly in "rumor" territory. Shacknews has contacted WB and will update as more information becomes available.