Robertson, 25, is 2-2 with a 5.54 ERA in 42 career big league relief appearances.
Drafted by the Twins in the third round of the 2006 draft, Robertson made his big league debut last season and appeared in just two games this year before being designated for assignment earlier this week.
Robertson has held left-handed batters to a .200 batting average in his career.
Robertson is the son of Jay Robertson, who works within the Nationals front office as a special assistant to the general manager.
With the addition of Robertson, the Nats now have 40 players on their 40-man roster.
On another note, the Yankees have announced that right-hander Chien-Ming Wang has exercised an out clause in his contract and has elected to become a free agent.
The former National signed a minor league deal with the Yankees this offseason, but now has chosen to hit the open market.
Anyone interested in a reunion?
Instant Update: Well, Wang wasn't on the open market long.
FOXsports.com's Ken Rosenthal is reporting Wang has signed with the Blue Jays and is expected to start for Toronto on Tuesday.