to keep as a pet is in the United States for private individuals. Under the Migratory Bird Treaty Act of 1918 , all native owls (such as Barn, Great Horned, or Snowy owls) are federally protected, making it a crime to possess them, their feathers, or even their eggs without specialized permits.
If you are interested in working with owls, there are narrow legal paths, but none allow for "pet" ownership. Legal Paths to Owning or Handling Owls
In the U.S., owls are managed under "stewardship" by the , meaning even permit holders do not technically "own" the bird. Owls as Pets - International Owl Center