Rogic started his playing career in FK Sloboda youth squad. In 1996. he becomes a part of OFK Beograd youth football school. He played in senior teams of FK Milicionar Beograd from 1999 to 2000, FK Kozara in Bosnia and Hercegovina and FK Radnicki Novi Beograd in 2002.

Rogic was one of the best students of Faculty of Sport and Physical Education in University of Belgrade. During his studies he started his coaching career working as the youngest coach of junior categories in FK Milicionar Beograd and FK Rad from 2003 to 2007.

Rogic began his senior coaching career in Malta, FC Floriana in season 2007/08. In August 2008, he became assistant coach of Serbia national football team, managed by Radomir Antic. He is officially the youngest coach of A team of Serbian and Yugoslavian football history and the youngest coach who participated in World Cup in South Africa in 2010. Serbia's World Cup qualification campaign began in 2008. Their qualification group featured former World Cup winners and 2006 FIFA World Cup runners-up France, traditionally powerful Romania, as well as Austria, Lithuania and the Faroe Islands. Serbia played consistently during the qualifiers and this led to the team automatically qualifying for the 2010 FIFA World Cup in South Africa. They confirmed qualification with a commanding 5–0 win at home against Romania. Like in 2006, Serbia went into the 2010 FIFA World Cup as the dark horses of the tournament. Key points justifying their potential surprise-team status included a star-studded defense that was composed by Nemanja Vidić, Neven Subotić, Aleksandar Kolarov and Branislav Ivanović. The captain of Serbia's 2010 World Cup campaign was stalwart Dejan Stanković, who became the only player to feature in a World Cup having played under three different national names (although he never changed nationality; this was a result of geopolitical events involving the identity of Yugoslavia). In their first tournament as an independent nation, they were to face Ghana, Germany and Australia. Their opening group game was against Ghana and chances came to both sides but a red card to Aleksandar Luković and a handball by substitute Zdravko Kuzmanović in the second half gave Ghana a penalty to take all three points at the death. Asamoah Gyan converted eight minutes from full-time and Serbia were defeated 1–0. In Serbia's second group match, they sensationally defeated Germany by a score of 1–0 with an acrobatic goal by Milan Jovanović late in the first half. FIFA's official YouTube channel called the win "the most famous day in Serbian football." Serbia only needed a single point to reach the knockout stages but were defeated by Australia 2–1 in an entertaining match where Serbia's dominance in the first half and in periods of the second half would have made it look like a Serbia victory. Australia scored 2 goals in the second half through Tim Cahill and Brett Holman. A late Marko Pantelić goal served only as a consolation. In 2011, he became assistant coach of Ghana national football team, working side by side with Goran Stevanovic. He also participated in 2012 Africa Cup of Nations in Gabon and Equatorial Guinea where Ghana national football team won fourth place. During 2012 he was assistant coach to Vladimir Vermezovic in FK Partizan, when the club qualified for the 2012–13 UEFA Europa League group stage. On 25 December 2012, it was announced that Radomir Antic signed a two-year contract with Chinese Super League side Shandong Luneng Taishan with Rogic as his assistant. Although leading Shandong Luneng, which finished the 12th in the 2012 season, to reach the second place of the league, they were released by Shandong on 21 December 2013. In September 2014, Rogic rejoins Serbia national football team managed by Dick Advocaat assisting him in planning activities, practices and games and opponents analysis. He returns to China in January 2015 as assistant coach for Radomir Antic in Hebei Zhongji. In May 2017 Aleksandar is hired by the Educational Center of Football Association of Serbia as a lecturer in UEFA A licence program for the field of "Standard situations" as part of the overall tactical preparation of football players. As of July 29, 2017, Rogic is hired as head coach of FCI Tallinn, 2016 Meistriliiga champion. In his first month as a head coach he won “Manager of the Month” award by Meistriliiga, achieving 6 victories in 7 games, especially winning derbies against FC Levadia Tallinn (2:1) and FC Flora (4:2). After the fusion of FCI Tallinn and FC Levadia Tallinn in November 2017, Aleksandar became the head coach of FC Levadia Tallinn, 9-time champion of Estonia.