Guillermo Rawson's parents were Dr. Aman Rawson, a doctor who had emigrated from the United States to Argentina, and Justina Rojo, a daughter of a wealthy family in San Juan, where Guillermo was born. His elder brother was the artist Franklin Rawson. After a Jesuit education in San Juan, Rawson graduated from the Medical Faculty of University of Buenos Aires in 1844. Rawson became interested in politics and democracy. In 1853 he was jailed for opposing Nazario Benavidez, the caudillo or de facto governor of San Juan. The following year he was a member of the
Paraná Congress, and from 1862 he was Interior Minister in the government of Bartolomé Mitre.
Apart from politics, Rawson was interested in medicine and hygiene. In 1876 he attended the Centennial Exposition in Philadelphia to present his work on public health in Buenos Aires, the most developed body of work on the subject at the time. In 1879, he was elected a member of the American Antiquarian Society.
Rawson spent a year in Paris in 1881 for medical treatment, before returning to Argentina. He returned to France for further treatment in 1885 and died in Paris in 1890.
The building of the first Medical School in Buenos Aires is named after him (Escuela Dr Guillermo Rawson).