He didn't have it when he arrived at the hospital ... How does he get this cut?
Actually, Ray did have the cut on his forehead from the very beginning of the accident.
As you can see there's blood trailing from the top of his forehead as he's trying to comfort his daughter at the construction site. The difference though is from when Ray actually arrived at the hospital, the blood had been cleaned away and all that was left was the cut.
And then, there's also the moment where Doctor Berthram comments on Ray's injuries --
Though it's never clarified that the doctor was actually referring to Ray's head injury instead of his face scrapes, they had been just talking about Ray's daughter's head injury and performing a CAT scan so, IMO, it's implied that Dr. Berthram was referring to Ray's head cut.
What is its significance?
The significance comes from the bandage that "magically" appeared over Ray's head cut and not necessarily the cut itself. From Ray's perspective (and the audience's) he was never treated by anyone -- he was there solely for his daughter and had been in the waiting room the entire time. This is the first obvious disconnect from Ray's experiences as perceived by the audience and what had actually been happening, suggesting that more is going on than what we the audience has seen (instead of just Ray's seemingly paranoia).