Two other photos - of what appeared to be a second deer - showed an arrow piercing through its face, just below both eyes. The deer in those photos was also upright and appeared to be walking.
The reward was initially $500 through the state's Turn-in-Poachers program, which pays for information in cases involving "illegal possession, killing, taking, and/or waste" of certain animals in the state, including bighorn sheep, moose, antelope, bears and game birds.
"Poaching wildlife and damaging habitats affects present and future generations of wildlife, impacts communities and the economy, and creates enforcement challenges," police said in a statement.
As of Sunday, the reward had increased to $2,000, after a local chapter of the Oregon Hunters Association offered an additional $1,500, the Oregonian reported.
Oregon State Police spokesman Kaito Raiser told the newspaper that they were still on the lookout for the affected deer - and that the arrows they had been stuck with were not the kind used by hunters.
"We've been unable to capture the deer to [tranquilize the animals and] remove the arrows," Raiser told the Oregonian. "You have to get very close to the deer, about 30 yards, for it to be effective, which is difficult for wild deer."
Anyone with any information in the case is asked to call Oregon Turn-in-Poachers at 1-800-452-7888 or Oregon State Police dispatch at 541-776-6111. Callers can remain anonymous, officials said.