As a youth player Šteinbors was a member of the Skonto Rigayouth academy. He was taken to the first teamin 2001. Even though he stayed in the club until 2004, due to high competition for the first keeper's place alongside that time Latvian internationalAndrejs Piedels, Šteinbors was unable to get a place in the usual starting line-up. In January 2004 Šteinbors joined another Latvian Higher League club FK Jūrmala, where he could finally settle down. Youngster showed some high-class performances and was regarded as one of the most talented Latvian youngsters. In December 2007 Šteinbors went on trial with the Football League Championship side Blackpool, impressing the coaching staff. On 16 January 2008, the German 2. Bundesliga club Augsburg reported that Šteinbors was on trial with them in their training camp in Faro, Portugal. However, on 31 January 2008, Šteinbors signed a loan deal with Blackpool until the end of the 2007–08 season with an option to extend it for another year. The loan was then extended and Šteinbors joined his countryman and current Latvian international Kaspars Gorkšs at Bloomfield Road. During his loan spell Šteinbors regularly played in the reserve team, but didn't make an appearance for the first team. After the end of the loan contract player returned to the Latvian Higher League, moving to FK Liepājas Metalurgs in 2009. During the 2009 and 2010 seasons he was the back-up keeper for the team behind experienced Viktors Spole. In 2011 Šteinbors finally claimed the first keeper's place, showing great performance and being included in the sportacents.com team of the season. All in all he played 53 league matches for Metalurgs. On 15 July 2012, Šteinbors moved to the South AfricanPremier Soccer League club Golden Arrows for the 2012–13 season. He started the season as the club's first keeper, but lost his place in the line-up in midseason, with the team struggling to show good results. In July 2013 Šteinbors moved to the Polish Ekstraklasa, signing a two-year contract with Górnik Zabrze after a successful trial period. He made his debut for the club on 17 August 2013 in a Polish Cup match against GKS Bełchatów, playing 90 minutes and keeping a clean-sheet.
