Săpunaru was born in Bucharest. A product of FC Național București, joining its youth system at the age of only 6, Săpunaru signed with FC Rapid București in July 2006. In the summer of 2008, he was sold for €2.5 million to FC Porto as a replacement for Chelsea-bound José Bosingwa and signed a five-year contract with the Primeira Liga club owning 50% of the player's rights – Romanian sources indicated the price was actually €6 million plus two players. During his debut campaign, Săpunaru was first-choice right-back as the northerners achieved a double, and scored his first goal in a 1–2 away loss against C.D. Nacional for the League Cup. In early February 2010, he was suspended in Portugal – as his teammate Hulk – following incidents during a 0–1 league defeat at S.L. Benfica, so he returned to his country for a five-month loan and moved to former side Rapid; he did not manage to be played regularly at Porto during that time but, following his return for 2010–11, became a very important first-team unit as they won three major titles, appearing in 40 official games in the process. On 17 February 2014, Săpunaru was condemned to pay a €90,000 fine for his participation in the assault of two stewards at the Estádio da Luz on 20 December 2009.
Zaragoza
On 31 August 2012, Săpunaru signed a one-year contract with La Liga club Real Zaragoza. He made his official debut on 16 September, playing the full 90 minutes in a 0–2 loss at Real Sociedad. In his first season in Aragon, Săpunaru started but also suffered team relegation. He also entered his name in the competition's history books, after breaking the record for the most bookings in a single campaign.
Elche
After initially hesitating because of the requests of his partner, Săpunaru signed a one-year deal at fellow league team Elche CF on 25 July 2013. He totalled only nine appearances in his only campaign and was also sent off twice, while his sole goal opened a 1–2 loss at Valencian Community neighbours Levante UD on 13 December. Elche could not support Săpunaru's €1 million wage demands, and released him on 21 August 2014. In October 2015, he took the club to court for the wages remaining in his contract.
Return to Romania
After four months back at Rapid, Săpunaru signed a season-long deal at CS Pandurii Târgu Jiu on 6 September 2015, including a clause that he could leave instantly if a foreign club wanted him. The following 21 July, he put pen to paper to a two-year contract with fellow league side FC Astra Giurgiu.
Kayserispor
On 1 July 2017, it was announced that Săpunaru signed a two-year deal with Turkish Süper Lig team Kayserispor. In January 2020 he returned back to the city from Capadocia for six months.
Begin 2019-20 season he signed for Denizlispor. He played in 15 competitive games before returning back to his former red-yellow side Kayserispor.
International career
Săpunaru made his debut for the Romania national team on 31 May 2008 against Montenegro, and was selected to the nation's squad at UEFA Euro 2008, although he did not play in the final stages. From June 2011 to November 2015, he did not appear in any games for his country due to a conflict with manager Victor Pițurcă. On 17 May 2016, Săpunaru was picked by manager Anghel Iordănescu for his Euro 2016 squad. He started at right-back in the group stage opener, a 1–2 loss against the hosts France. In September 2019, after amassing 36 caps over the course of eleven years, Săpunaru announced his retirement from the national team.
