Torje made his debut during the 2005–06 season for Politehnica Timișoara against Argeș Pitești and scored on his second match, against Farul Constanța. He was promoted in the first squad by Gheorghe Hagi, manager of Timișoara at that time.
Dinamo Bucharest
On 15 January 2008, Torje signed a five-year contract with Dinamo București. The reported transfer fee was $2.5 million. He played his 100th match in Liga I for Dinamo on 6 May 2011, in a defeat against CFR Cluj.
On 30 August 2011, he signed a five-year contract with Serie A club Udinese for an undisclosed fee, rumored to be around €7 million. He played his first game in Serie A against U.S. Lecce, on 11 September 2011, even though he had only five days of training with his new team, and he had an impressive performance, suggesting that Alexis Sánchez may not be as irreplaceable as first thought. On 5 February 2012, Torje scored his first goal in the Serie A in a 3–2 loss against Fiorentina. On 24 March, in a game against Palermo he equalized the score in the 85th minute, giving his team a 1–1 draw.
In order to get more playing time, on 8 June 2012, Torje signed for La Liga side Granada on a season long loan. He made his debut for the Spanish team on 20 August, in a 1–0 away defeat against Rayo Vallecano. Halfway through the season Torje was considered as one of the most successful transfers in the 2012–13 La Liga, and he became a crucial part of the team. He was praised for his performance in the 1–0 victory over La Liga champions, Real Madrid, on 2 February 2013.
Loan to Espanyol
On 2 September 2013, Torje began his second journey in La Liga this time being loaned at the second major club in Barcelona, RCD Espanyol. He made his debut for the club on 23 September in a 3–2 win over Athletic Bilbao. He played only 12 games for Espanyol, six in the starting lineup and six as a substitute, without scoring a goal. Thus, the Spanish side didn't activate the option to buy the player at the end of the loaning period.
Later years
In June 2014, Turkish Super Lig side Torku Konyaspor announced that they reached an agreement with Udinese to loan the player for a season. On 2 February 2018, he rejoined Dinamo București on loan until the end of the 2017–18 season. On 1 September 2018, he returned to Turkey, signing with Sivasspor. On 4 February 2020, he signed a contract with Superleague club AEL. On 22 June 2020, he scored a brace, helping to a 3–1 home win against Volos for the second game of the 2019–20 Superleague playoffs.
International career
Torje was the captain of the Romania under-21 football team side. He also made his debut for the senior side in a friendly match against Albania on 3 September 2010. He scored his first international goal in a match against Cyprus. On 2 September 2011, he scored twice in a 2–0 win over Luxembourg. Torje scored his first competitive goals in a 2–0 win over Luxembourg during the UEFA Euro 2012 qualifying. He scored three goals during the 2014 World Cup qualifiers as Romania reached the play-offs only to lose to Greece. He did not score in Romania's successful qualification for UEFA Euro 2016 but was chosen in the tournament's 23-man squad. He started in Romania's 1–1 draw to Switzerland and made brief appearances as a substitute in Romania's defeats to France and Albania with the latter one confirming their elimination from the tournament.
