Abbott was claimed off waivers by the Nationals on Wednesday, Jessica Camerato of MLB.com reports.
Abbott was traded from the Cubs to the Giants on April 21, but he was recently cast off San Francisco's 40-man roster. He'll land with the Nationals and has been optioned to Triple-A Rochester to begin his time with the organization. He's allowed three runs while striking out six in six innings over two Triple-A starts this year.