Parga began his political career when he was elected state president of the Republican Youth in 1957, a post to which he was reelected in 1960 and 1964.
In 1961, Parga became the first Puerto Rican to be named as part of the United States Republican Youth National Committee.
In 1968, Parga ran unsuccessfully for an at-large seat in the Puerto Rico House of Representatives under the Republican Party, which would disappear following that year's elections.
From 1975 to 1976, Parga served as Press Aide to Carlos Romero Barceló, who was Mayor of San Juan at the time.
He also served as Communications Advisor to another Mayor of San Juan, Baltasar Corrada del Río, from 1985 to 1988.
From 1993 to 1994 he also served as Director of the Press, Communications, and Public Relations Office of the Senate of Puerto Rico.
[3] For their loyalty, they became known as "Los Auténticos", which in turn, ignited a series of schemes to coerce them into supporting Rosselló.
In November 2005, it was revealed that the Puerto Rico Capitol's surveillance camera system was allegedly misused to blackmail fellow Senator Carlos Díaz, one of the so-called "Auténticos".