"Batman does not get his own ring. He temporarily borrows Hal Jordan's as an attempt at psychotherapy. Nor is the cover a piece of fan art. It was actually an alternate cover to the issue Green Lantern Vol 4, #9, "Branded" by Geoff Johns. The cover was done by Ethan Van Sciver.
"Branded" - Batman calls on Green Lantern to take on a new version of an old foe - the Tattooed Man. This one is in the Cityside Motel in Gotham City, and has been murdering people, including Lou Rosen who was cheating on his wife. While Green Lantern takes on his tattoos, Batman takes out the man himself. Back in the Batcave, Hal has Bruce try on the ring, to try and help him overcome his inner demons. Bruce conjurs up images of bats a first, but then gains control and forms a vision of his parents. Batman tells him he's not ready to give up his darkness, but thanks anyway and they part ways."