Rodić played his first professional match for OFK Beograd on 26 April 2009, against Partizan at the age of 18. Almost two years later, on 25 April 2012, he was named left-back in Sportal's ideal team of Round 26 in the 2011–12 Serbian SuperLiga.[2]
In August 2015, Rodić signed with Krylia Sovetov. Over the course of two seasons, Rodić got back into competitive shape.[4] After two years with Krylia Sovetov, Rodić thanked the fans and commented that he was happy to play for Krylia, but that he missed his family in Serbia.[4]
Red Star Belgrade
On 21 July 2017, Rodić signed a three-year contract with Serbian side Red Star Belgrade.[5] Red Star had paid approximately €250,000 to Krylia Sovetov for Rodić's transfer.[4] He played in Red Star's 2017–18 UEFA Europa League campaign under coach Vladan Milojević. On 19 October 2017, Rodić got a red card in the Group H home match against Arsenal, which Red Star lost 1–0.[6] On 12 March 2019, he extended his contract with Red Star to the summer of 2022.[7]
In May 2018 he was named in Serbia's preliminary squad for the 2018 FIFA World Cup in Russia.[9]
On 4 June, he made his international debut in a friendly match against Chile, coming on as a substitute for Aleksandar Kolarov in the 80th minute.[10]
Rodić was selected in Serbia’s squad for the 2018 World Cup,[11] but he failed to make any appearances there.