Born in Ulcinj, Rudović started playing football with Otrant in his home town at the age of 6. Later he moved to Mornar Bar, where he stayed for two years. Finally, he joined Mogren where he ended his youth career and made his first senior appearances with the club in 2013. Rudović signed a one-year deal with PSV Eindhoven in 2014.[4] As a club member, he usually played with reserves, making his professional debut for Jong PSV player in the second division on 19 September 2014 in a 0–2 home defeat against Sparta Rotterdam. After the end of contract he left the club in summer 2015, after which he joined Mladost Podgorica.[5] Making 29 appearances with 2 goals at total in both domestic competitions mostly as a back-up player,[6] Rudović contributed to winning the Montenegrin First League for 2015–16 season.[7] Next summer, he left the club and moved to OFK Petrovac.[8]
On 17 August 2017, Rudović signed with the Serbian SuperLiga side Spartak Subotica, peening a three-year professional contract with new club.[2] Making a single appearance with a goal in the Serbian Cup match against Polet Lipljan,[9] Rudović released by the club in December same year.[10] At the beginning of 2018, Rudović signed with Kom.[11]
He scored his first league goal for Mohammedan on 8 March 2022 against Sreenidi Deccan in their 3–1 win.[14] Under Nikola Stojanović's captaincy, Mohammedan for the first time, ran for their maiden national league title in 2021–22 I-League season, but finished as runners-up after a 2–1 defeat to Gokulam Kerala at the end.[15]