There was no place, however, for Carlos Tevez among the forwards which include his Manchester City team-mate Sergio Aguero, Spain-based Lionel Messi and Gonzalo Higuain and Napoli's Ezequiel Lavezzi.
Coach Alejandro Sabella named 18 foreign-based players on Friday night and is expected to boost the numbers with some from the domestic league in a squad to face Ecuador at River Plate stadium in Buenos Aires on June 2.
Rodriguez has had a brilliant six months helping La U win the Copa Sudamericana, South America's equivalent to the Europe League, in December and reach the Copa Libertadores quarter-finals this month.
The 26-year-old, who has also played as a right-back, has scored some key goals for the 2011 Chilean champions, generally from outside the box coming through from deep positions.
Argentina are joint top of the South American group with Uruguay and Venezuela on seven points. They have a bye in the following round of qualifiers on June 9 when they will meet Brazil in a friendly in New Jersey.