Born in Penrith, New South Wales, Asiata is of Samoan descent and played his junior football for the Wentworthville Magpies, attending Patrician Brothers' College, Blacktown.
In 2009, Asiata was a member of the Parramatta Eels side that finished runners-up in the Harold Matthews Cup. In 2010, he played with the Western Sydney Academy in the S.G. Ball Cup before being signed by the Sydney Roosters. He played for the Roosters' S.G. Ball team in 2011 and played for their National Youth Competition (NYC) team in 2012 and 2013. At the end of 2013, Asiata was named at lock in the 2013 NYC team of the year. In November 2013 Asiata signed a 2-year contract with the North Queensland Cowboys, starting in 2014, following his Roosters NYC coach, Paul Green, to the Cowboys.
Asiata started the year playing for the Cowboys Queensland Cup affiliate, the Mackay Cutters. He would play 18 games for them in 2014, scoring 5 tries.
In round 12 of the 2014 NRL season, Asiata made his debut for the Cowboys, against the Melbourne Storm, off interchange bench in the Cowboys 22-0 win at 1300SMILES Stadium. Asiata finished his debut year in the NRL with 6 matches for the Cowboys. On 14 October 2014, Asiata was named the Cowboys' rookie of the year at their annual presentation ball.
On 31 January and 1 February, Asiata played for the Cowboys in the 2015 NRL Auckland Nines. On 27 April, he was named in Samoa's 18-man squad to face Tonga in the 2015 Polynesian Cup. He was the side's 18th man and did not participate in the match. In round 9, he made his first start in the NRL, in the Cowboys' 23-16 victory over the Canterbury-Bankstown Bulldogs. On 21 May, he re-signed with the Cowboys on a 2-year contract until the end of the 2017 season. On 4 October, in the Cowboys Queensland derby 2015 NRL Grand Final match against the Brisbane Broncos, Asiata played off the interchange bench in the Cowboys' golden-point 17-16 win. He finished off his premiership winning 2015 season having played in 25 matches.
On 2 February, Asiata was named in the Cowboys' 2016 NRL Auckland Nines squad. On 21 February, he was a member of the Cowboys' 2016 World Club Challenge winning side, coming off the bench in the side's 38-4 victory over the Leeds Rhinos at Headingley Stadium. On 7 May, he made his international debut for Samoa against Tonga in the 2016 Polynesian Cup. Asiata played 19 games in 2016, which included his 3rd career start, against the Canberra Raiders in Round 18.
In Round 7 of the 2017 NRL season, Asiata started at halfback against the St George Illawarra Dragons, replacing the injured Johnathan Thurston. In the 26-20 loss, Asiata finished the game with two try-assists and two line-break assists. In his 76th match, in the Cowboys' semi-final against the Parramatta Eels, Asiata scored his first ever NRL try.
North Queensland Cowboys Club Person of the Year: 2016
North Queensland Cowboys Rookie of the Year: 2014
NYC Team of the Year: 2013
2015 NRL Grand Final: North Queensland Cowboys – WinnersStatistics are correct to the end of the 2016 season
2016 World Club Challenge: North Queensland Cowboys – Winners