Cesić began his footballing career with FC Sveta Lucia in late 2009. He quickly became an important player and a proficient goalscorer for the team, playing a crucial role in their 2010-11 Liga 2 Juliana win. In the summer of 2011, he was bought by A.C. Ciconia, where he has played since. Cesić has been an important factor to the success of A.C. Ciconia, as a versatile and creative midfielder skilled at free kicks and long passes. He is also quite a proficient goalscorer; for example, in the 2014-15 Liga 1 Juliana, he scored 17 goals. Since mid-2013, Cesić is also the squad captain of A.C. Ciconia.
Cesić played for the Juliana national under-20 football team in late 2010 and early 2011. In late 2011, he made his debut for the senior Juliana national football team, where he has also been an important player and a consistent goalscorer. For both his club and country, Cesić quite frequently takes free kicks.