This is Black Rock Shooter (anime & character both have the name). It originally was a drawing from Ryohei Fuke on Pivix. This later spawned an OVA and subsequent anime series in 2012 and also a PSP game
Black★Rock Shooter (ブラック★ロックシューター Burakku Rokku Shūtā?) [...] revolves around its eponymous character, a mysterious black haired girl with a blazing blue eye.
The original illustration inspired a song of the same name by Supercell, which gained popularity on the Nico Nico Douga website. A 50-minute original video animation based on the franchise was produced by Yutaka Yamamoto's studio Ordet, written by Nagaru Tanigawa and Shinobu Yoshioka, and directed by Shinobu Yoshioka. A "Pilot Edition" was released on DVD and Blu-ray Disc in September 2009, before the full version was released on DVDs bundled with select magazines from July 24, 2010, subtitled in seven languages, followed by a retail release on December 17, 2010. An eight-episode television anime series, produced by Ordet and Sanzigen, aired on Fuji TV's Noitamina programming block between February 2 and March 22, 2012. The franchise has also spawned several manga series and a video game for the PlayStation Portable titled Black Rock Shooter: The Game, each set in their own universe.
If you want to watch/play you don't have to worry about the order too much as the stories are separate