Rodriguez, 26, went 0-1 with a 4.00 ERA in 17 relief appearances with the Nationals, totaling 18 innings. He limited opponents to a .203 batting average against, including a .194 mark by right-handers and a .211 mark by left-handers. He was designated for assignment June 4.
He has pitched all or part of five Major League seasons with the Athletics and Nationals, and has a career 4.23 ERA in 143 relief appearances. Rodriguez was not expected to arrive in Chicago in time for Wednesday's game.
Dickson, 22, a 35th-round pick in the 2011 Draft, was 2-2 with a 6.88 ERA in 11 appearances (three starts) with Class A Kane County.
Sanchez, 24, was 0-1 with a 9.82 ERA in six relief appearances at Iowa. He was claimed off waivers from the Cardinals on May 21.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.