He started his club career at Skonto-Metāls. He made his debut in senior football at an early age, being just 16 years old. Together with Skonto Riga he won 7 national titles. In 1995, he made his debut for Latvia and soon he became a regular member of the side. While playing with Skonto, Stepanovs played against teams, like Inter Milan, Barcelona and Chelsea. In these games, Skonto and Stepanovs performed well. In 2000, he attracted interest from many European teams.
In 2000, Arsenal captain Tony Adams was injured, prompting Arsène Wenger to sign Stepanovs for a transfer fee of £1.35 million. He started the season well, scoring a goal for Arsenal in a 2-1 League Cup defeat against Ipswich Town on his debut. His playing time grew until a match against Manchester United, when both sides were battling for the Premier League title. Arsenal lost this game 6-1 and their chances of winning the title were hit. After this disappointing performance, Stepanovs played only once again that season in a game against Manchester City. He recovered to make 6 Premier League appearances the following season as Arsenal won the 2001–02 FA Premier League. Six would not normally be enough to earn a medal but he was an unused substitute on the day Arsenal clinched the title against Manchester United at Old Trafford, the scene of his lowest point the season before. Arsenal also won the FA Cup in 2002 and 2003 but Stepanovs was left out of both match day squads. He contributed to their 2002 triumph when featuring in a game against Newcastle United during their run. Overall, he played just 17 times in the league for Arsenal, all of them starts, and 31 times in all competitions.
Later years
After unsuccessful years with Arsenal, Stepanovs was moved to K.S.K. Beveren, which had co-operation agreement with the English club. There he gained back some confidence and he was again in good shape. Stepanovs played well in the Latvian national team, helping it to qualify for Euro 2004 where he played in all of Latvia's three games. After Euro 2004, Stepanovs joined Grasshopper Club Zürich. There he played for 2 seasons, but later he was released. In 2006, he came back to Latvia and played some games for FK Jūrmala. On 26 January 2007 he moved to Danish Premier League side Esbjerg fB on a free transfer, but after just a year he moved to the Russian FC Shinnik Yaroslavl. He was released by Shinnik on July 9, 2008 and in April 2009 he signed for Latvian side RFS/Olimps, but a year later re-joined his previous team FK Jūrmala. He played there for two seasons, with Stepanovs making 25 league appearances, scoring a solitary goal. In August 2011, the player announced his retirement from professional football. On 10 August 2011 Stepanovs was called up to the Latvia national football team for a friendly match against Finland. He played his 100th and last match for Latvia then, and was honoured during the match for his long-term commitment to the national squad.
Coaching career
During his time at FK Jūrmala, Stepanovs worked as a player/coach assisting the club's manager Vladimirs Babičevs. In March 2012, Stepanovs was appointed as the manager of Latvia national under-17 football team.