Sopoaga attended Samoana High School in Pago Pago, Pūala'umuli School District, American Samoa and was a letterman in football, basketball, and baseball. In football, he was a two-time All-League selection and as a senior, he was named the League's Defensive Player of the Year. He played rugby league growing up in Samoa. Isaac also attributes his strong throwing arm, reportedly being able to throw the ball 78 yards flat footed, to throwing 1–2 pound rocks at coconuts up to 70 feet high hanging from the trees. He would eventually develop enough strength and accuracy to knock down five or six coconuts in a matter of five minutes according to his own account.
Sopoaga began his collegiate career at the College of the Canyons. As a freshman, he was suspended for two games after hitting an opposing player. In his sophomore season in 2000, he recorded 31 sacks, which still stands as the single-season record in California community college football. He then decided to sit out the 2001 season to establish residency. Sopoaga was inducted into the College of the Canyons Athletic Hall of Fame in 2011.
He then attended the University of Hawaii, where he started his junior and senior years, and collected 128 tackles (70 solos) with four sacks for minus 28 yards, 15 stops for losses of 56 yards, eleven quarterback pressures, a pair of fumble recoveries, two forced fumbles and three pass deflections in 25 games with the Warriors.
Projected to be an early second round selection, Sopoaga was ranked as the No. 4 defensive tackle available in the 2004 NFL Draft. As of 2013, Sopoaga is one of only fifteen prospects to repeat more than 40 lifts at the 225-pound (102 kg) bench press at the NFL Scouting Combine since 1999. While he was noted for his "outstanding strength" and quickness off the snap, scouts criticized his tendency to "get tall, which negates his power," as well as his lack of hand technique. Sopoaga was eventually selected in the fourth round, 104th overall, by the San Francisco 49ers. He was the highest selected Hawaii Warriors defensive lineman since Al Noga in 1988.
He was drafted by the San Francisco 49ers in the 4th round (104 overall) in the 2004 NFL Draft. Sopoaga missed the entire 2004 season with an injury. In 2008, the 49ers stated that they would use Sopoaga as a defensive end. For the 2010 season, Sopoaga started at left defensive end in the 49ers 3-4 defense.
In the October 17, 2010 game against the Oakland Raiders, Sopoaga lined up as a fullback and successfully blocked for Frank Gore deep in the red zone near the end of the game. The play resulted in a first down which allowed the 49ers who were leading 17 to 9 to run out the clock and win the game. In a Monday press conference following the game 49ers head coach Mike Singletary said that putting Sopoaga in as fullback was an idea he presented to former offensive coordinator Jimmy Raye earlier in 2010. Singletary gave credit to Bill Walsh's playing of guard Guy McIntyre as a fullback rather than Mike Ditka's playing of lineman William "The Fridge" Perry as a fullback on Singletary's Chicago Bears team, since Walsh started the trend and Ditka followed. Prior to the 2011 season the 49ers parted ways with nose tackle Aubrayo Franklin, leaving a void at the nose tackle position which was filled by Sopoaga. On October 30, 2011, playing from fullback position, Sopoaga caught a pass for a key first down in the fourth quarter of the 49ers' 20-10 victory over the Cleveland Browns.
Sopoaga signed a three-year, $12 million deal with the Philadelphia Eagles on March 12, 2013.
On October 29, 2013, Sopoaga was traded to the New England Patriots along with a sixth round pick for a fifth round draft pick in the 2014 draft.
Soon after working out for the Arizona Cardinals on August 20, 2014, Sopoaga officially signed with them. The Cardinals released Sopoaga on August 30, 2014.
A native of American Samoa, Sopoaga was raised in the village of Fagasa, an isolated fishing community. He is one of nine children (four brothers, four sisters) of Suitupe and Lagiselota Sopoaga.
He owns a second home in Hawaii, where he spends the off-season.