Destro became the team's top goalscorer with 12 goals, followed by Emanuele Calaiò's 11 goals. On 20 June 2012, Siena purchased half of Destro's registration rights from Genoa for €1.3 million. However, after Roma formed an agreement with both Genoa and Siena, Genoa bought back Destro from Siena for €7.5 million million (€6 million cash plus half of Eugenio Lamanna) in order to complete the deal.
On 30 July 2012, Roma announced it had signed Destro from Genoa in a temporary deal for €11.5 million (€8.5 million cash plus half of the rights to both Giammario Piscitella and Valerio Verre) with the option to purchase him outright for an additional €4.5 million (which meant Destro would cost Roma €16 million in total if the purchase was completed). Destro would replace the Liverpool-bound striker Fabio Borini, whom Roma just sold for €13.3 million. Destro made his Roma debut on 2 September 2012 in a 3–1 Serie A win away against Internazionale. He scored his first goal for the Giallorossi in a 4–1 home match against Palermo on 4 November. He also received his first red card with the club in the same match after receiving two bookings from the referee, the second of which was for taking off his shirt when celebrating his goal. Destro played 21 Serie A matches for Roma in his first season, many in which he came on as a substitute, and scored six goals. Roma finished a distant sixth in Serie A, but did reach the final of Coppa Italia. Destro scored five goals en route, making him top-scorer for the tournament. However, Lazio edged a 1–0 win over Roma in the final.
On 15 August 2012, he made his debut with the Italy national team, starting in a 1–2 friendly loss to England at Wembley Stadium. He was substituted off for fellow debutant Diego Fabbrini in the 84th minute. In Destro's third appearance, on 11 September, he scored his first international goal in the first five minutes of Italy's 2–0 win against Malta at the Stadio Alberto Braglia in Modena, in Italy's second 2014 FIFA World Cup qualifying match.