Born in Lucerne, Stocker began his youth career with SC Kriens, playing there between 1996 and December 2005.

[5] Having played in 12 test matches he made his team debut in that season's Swiss Cup semi-final, a home game in the St. Jakob-Park on 27 February 2008, as Basel won 1–0 against Thun.

[6] One week later, in the away match against the same opponent, Stocker played his league debut, as Basel won 3–1 thanks to a hat-trick from Eren Derdiyok.

[10] Basel joined the 2008–09 UEFA Champions League in the second qualifying round and with an aggregate score of 5–3 they eliminated IFK Göteborg.

In the Cup Final he scored a brace, the feams first and fifth goals as Basel won 6–0 against FC Lausanne-Sport.

[16] In the 2010–11 season Stocker played 26 League games, marking seven goals, and he won his third championship medal with the club.

In the 2011–12 season he returned into the team on 3 December 2011 during the 1–0 home victory against FC Luzern and on the same day it was announced that his contract had been extended until the end of June 2016.

During the first leg match in the Round of 16 on 22 February 2012 against Bayern Munich he was substituted in and scored the winning goal.

this was also his third Double because Basel also won the Swiss Cup[22] During the 2012–13 season Stocker had another highlight in his football career.

[30] Stocker reportedly received a four-year contract after Hertha and FC Basel agreed on a transfer fee of around €5 million.

[31] On 10 January 2018, FC Basel announced that Stocker would return to the club, signing a three-and-a-half-year contract dated up until June 2021.

[33] Stocker played in five cup games and scored the two goals, these both being during the extra time in the match against Sion.

[34] On 17 May 2022, Basel announced that Stocker would retire from playing at the end of the 2021–22 season and will remain at the club as an assistant to the sporting director.

His debut for the U21 was on 26 March 2008 in the UEFA European Under-21 Football Championship qualification Group 5 2–1 away defeat against Macedonia Under-21.

He made his debut for Switzerland in Ottmar Hitzfeld's first match as manager, on 20 August 2008 against Cyprus at Stade de Genève.

Stocker was included in Switzerland's squad for the 2014 FIFA World Cup, making one appearance, starting in the opening match against Ecuador before being substituted out at halftime.