Vrančić started playing football at a local club, before joining youth academy of Mainz 05 in 2004.

[11] He made his competitive debut for the club in DFB-Pokal game against TuS Erndtebrück on 7 August.

[14] In June 2017, Vrančić joined English outfit Norwich City on a three-year deal.

[16] On 19 September, he scored a brace in EFL Cup game against Brentford, his first goals for the side.

[18] Vrančić was an important piece in Norwich City's conquest of Championship title, his first trophy with the club, which was secured on 5 May 2019 and earned them promotion to Premier League.

[30][31] He permanently signed for Rijeka in February 2023, being afterwards loaned to Bosnian Premier League side Sarajevo.

[32] On 11 June 2024, Vrančić signed with Regionalliga Südwest club Eintracht Frankfurt II.

[34] In June 2015, his request to change sports citizenship from German to Bosnian was approved by FIFA.

[35] Subsequently, he received his first senior call-up in August 2015, for UEFA Euro 2016 qualifiers against Belgium and Andorra.