Sivonjić started his senior career in top flight, debuting for Kamen Ingrad on 21 May 2005.

Following Kamen's relegation at the end of the 2006–07 season, he was bought by Inter Zaprešić and made his first appearance for the club on 14 September 2007 against Međimurje, netting a brace in his debut.

In the 2008–09 season Sivonjić was Inter's top goalscorer before he was transferred to Croatian champions Dinamo Zagreb on 18 December 2008.

In his debut season for Dinamo Sivonjič made 14 league and 3 more in the Croatian Cup, scoring 4 goals.

Between 2014 and 2018 Sivonjić played for a string of lower-tier German clubs[2] followed by a season at the Belgian 6th tier team KAV Dendermonde.