He was born to an old family of the local nobility of Loreto Aprutino (province of Pescara), and was educated in Pisa, graduating in agricultural sciences from the University of Pisa in 1912. Acerbo's affiliation with the Freemasons led him to become an advocate of irredentism and Italy's entry to World War I. When war exploded upon the continent, he volunteered for military service. By the end of the war, he was decorated with three silver medals for military valor and promoted to the rank of captain.
Acerbo resumed his work as an assistant professor in the faculty of economics, and planned for a university career. At the same time, he promoted the Association of Servicemen of Teramo and Chieti (l'Associazione dei combattenti di Teramo e Chieti), which broke away from the national association after the election of 1919 and became the Provincial Combat Group (il Fascio di combattimento provinciale).
Elected to the Italian Chamber of Deputies in 1921 with the "national bloc", he acted as a mediator between local conservative forces and the Blackshirts; on a national level, Acerbo ensured peace in the open conflict between the Italian Socialist Party and Fascists, and was elected to a leadership position inside the National Fascist Party (PNF). During the March on Rome, Acerbo presided the Chamber as the coup d'état unfolded, and acted as the link between the PNF and King Victor Emmanuel III. He then accompanied Mussolini as he was designated Prime Minister, and became his undersecretary.
He made the Acerbo Law pass in November 1923; he was again deputy in 1924, winning his nobiliar title. Acerbo was marginally involved in the inquiry over Giacomo Matteotti's killing, and left his position in the government. In 1924 he instituted the Coppa Acerbo in memory of his brother Tito Acerbo (a war hero). Giacomo Acerbo was elected vicepresident of the Chamber in 1926, and was Agriculture and Forestry Minister from 1929, dedicating himself to projects for universally-extended drainage. Together with Gabriele D'Annunzio, he contributed to the creation of Pescara Province in January 1927.
Acerbo became head of the Economics and Commerce Faculty at the University of Rome in 1934, and, from 1935 to 1943, president of the International Agricultural Institute. A member of the Grand Council of Fascism, he was a spokesman for the project that torned the Chamber into a representative of Fasci and Corporazioni.
When World War II began and Italy joined the Nazi German offensive, Acerbo served as member of the Italian Army General Staff during the marginal Italian maneuver in the Battle of France, and the Greek campaign. He was also Minister of Finance from February 1943.
On July 25, Acerbo sided with Dino Grandi when the latter attempted to topple Mussolini and take Italy out of the war. He voted in favor of the law that stripped Il Duce of his powers, and took refuge in his homeregion, the Allied-occupied Abruzzo - after Mussolini regained some standing with help from the Nazis, establishing the Italian Social Republic, one that proscribed all opponents (including Acerbo) during the Verona trial. Captured by the Resistance, he was sentenced to death by the High Court of Justice, a verdict lessened to 48 years in prison. This sentence too was overturned, and Acerbo's name was cleared in 1951, enabling him to resume his teaching career. He received numerous distinctions and titles in academia, and was awarded a gold medal (in Education, Culture, and Arts) by President Antonio Segni.
Acerbo died in Rome in 1969.
He is also remembered for his passion as a collector of ancient pottery, and created a Gallery dedicated to ceramics of the Abruzzo.