It would depend on both the state it happened in, and that state's specific penalties for Animal Cruelty. Since raping an eagle isn't killing, and technically wouldn't be considered rape because it is, afterall, an animal.
I would estimate that it would automatically be tried as a felony cruelty to animals charge because of the bald eagle being our nation's bird, and one would have to be one sick individual to rape a bald eagle, or any animal or human, for that matter.