Civoniceva played his club football for the Brisbane Broncos, with whom he won the 1998, 2000 and 2006 NRL Premierships, as well as for the Penrith Panthers, whom he captained.

He won the club's Rookie of the Year award in 1998 and went on to play from the bench in Brisbane's 1998 NRL grand final win at the end of the season.

Civoniceva missed the Broncos grand final victory in 2000 due to injury, as well as Australia's 2000 World Cup campaign.

Having won the 2000 NRL Premiership, the Broncos travelled to England to play against 2000's Super League V Champions, St Helens R.F.C.

As 2006 NRL Premiers, the Brisbane Broncos travelled to England to face 2006 Super League champions, St Helens R.F.C.

[10] In round 8 of NRL season 2007, Civoniceva played his 200th game for the Brisbane club,[11] becoming only the eighth Broncos player to ever do so.

[15] Civoniceva's move to New South Wales and another NRL team rather than relocating to England allowed him to continue to be available to represent both Australia and Queensland.

As a result, he missed Penrith's first qualifying final, where, despite a brave effort, the Panthers lost by just two points against the Canberra Raiders.

[20] Civoniceva's stint at Penrith ended on a low, with the Panthers failing to qualify for the semi-finals, and thrashed by the St. George Illawarra Dragons, 32–12, at Round 26.

Civoniceva was selected in the Australian team to compete in the end of season 2004 Rugby League Tri-Nations tournament.

Civoniceva was again selected to play for the Australia national team as a prop forward the 2007 ANZAC Test match victory against New Zealand.

At the end of 2013 he was selected to travel to the United Kingdom and represent Fiji, the country of his birth, in the 2013 Rugby League World Cup.