At club level Soria was a one-club man, playing his entire career for Bolívar, where he won 8 national titles. He played in 451 games netting 52 goals. He also participated in 93 Copa Libertadores matches and scored 4 goals. Soria is third player with more appearances in the history of this international competition.
Between 1989 and 2000 Soria has earned 51 caps and one goal for the Bolivia national football team. Among the most important tournaments at international level, Soria played in the 1994 FIFA World Cup and Copa America 1997, where he was the national team's captain. His only goal came in a 1998 FIFA World Cup Qualifier on February 12, 1997 against Chile, when he opened the score in the 27th minute.