Hill is 3-3 with a 4.68 ERA in 12 starts for Syracuse this year.
Jordan is 0-2 with a 6.43 ERA in three Major League outings this year. He threw 3 1/3 scoreless innings on Tuesday in relief of Max Scherzer.
The Nationals acquired the No. 66 international signing bonus slot for 2015-16 from the Red Sox in exchange for right-hander Ramses Rosario, the club announced Wednesday.
Rosario, 19, has made 34 appearances in the Dominican Summer League since 2013. He allowed 16 earned runs in 16 innings over nine outings in 2015.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.