Borghi started his sports career as a professional baseball player, but turned to soccer instead. He chose the position of goalkeeper because he felt he lacked the necessary ball skills to play any other position. In fact, when he was in goal, he never kicked the ball, even for goal kicks (someone else took them); instead, thanks to his arm strength from playing baseball, he always threw the ball after he made a save. He played professionally for St. Louis Simpkins-Ford and helped them win the U.S. Open Cup in 1948 and 1950.
He was selected to the U.S. national team in 1949 and played in four World Cup qualifying matches as well as all three games in the 1950 World Cup. He also appeared for the U.S. in 1954 World Cup qualifying against Mexico. Borghi was inducted into the United States National Soccer Hall of Fame in 1976 along with the rest of his 1950 teammates.
After his retirement from the sport, he became a director of a funeral home in St. Louis until 2003. In January 2004, he and the four other living members of the 1950 World Cup Team (Walter Bahr, Harry Keough, Gino Pariani and John Souza) were recognized as Honorary All-Americas by the National Soccer Coaches Association of America at its annual convention in Charlotte, N.C.