Aleksandrs Koļinko was born in Riga and started his career in 1994, playing for Skonto Riga reserve team Interskonto, which was renamed Skonto-Metāls in 1995. After two seasons in the reserve team Koļinko broke through to Skonto Riga first team in 1996. In 1997 Koļinko participated in the UEFA Champions League qualification match against FC Barcelona, but eventually he became a first eleven player just in 1999, after the retirement of Oļegs Karavajevs.
Koļinko, a goalkeeper, made his name in the football world during a spell at English club Crystal Palace, where his appearances were limited due to his inconsistent form. He joined the club in 2000 alongside his international team-mate Andrejs Rubins. He could make brilliant saves one moment, but terrible blunders the next. Reportedly, he was disciplined by the club after, while on the substitutes' bench, he was accused of laughing at a goal his own team had conceded and punched in the face by manager Trevor Francis. Francis was later fined by the club and the Football Association for his actions.
In 2003 Koļinko was released by Crystal Palace and he joined the Russian Premier League club FC Rostov. Playing there for two seasons, Koļinko showed good performance and transferred to Rubin Kazan in January 2005. At that time he was certainly one of the best goalkeepers in the Russian Premier League. In 2006 Koļinko was named Latvian Footballer of the Year. He was dismissed from Kazan for an unexplained reason before the 2008 season, playing there for 2 years. After his release, Koļinko joined the Latvian Higher League club JFK Olimps, but after just playing 6 matches he left the club, following the interest from several clubs abroad.
In May 2009 he signed a contract for 30 days with Dinamo București. At the end of the season the board announced he would not be offered a new contract. In August 2008 he went on trial with Notts County in England, but didn't stay with the club. In the summer transfer period he signed a contract with the Latvian Higher League club FK Ventspils. In December 2009 he extended his contract with Ventspils for another year. Despite this fact, he was linked with a move to the Russian club FC Sibir Novosibirsk but just after a few days it was announced that he would not go on trial with the team.
In August 2010 Koļinko joined the Russian Premier League club PFC Spartak Nalchik on trial and signed a one-year contract with them on 26 August 2010. He played 8 matches there battling with Otto Fredrikson for the first keeper's role. Despite earning the number 1 role and playing some really good matches, after the season he was released. In February 2011 Koļinko joined the Russian National Football League club Baltika Kaliningrad, signing a contract for one and a half season. His contract was then extended till the end of the 2014–15 Russian National Football League season.
In June 2015 Koļinko returned to the Latvian Higher League, joining Spartaks Jūrmala prior to their Europa League debut. He made his debut as Spartaks beat Mladost Podgorica 3-1 in the first round of the tournament. Koļinko made his Latvian Higher League come-back on 12 July 2015 in a 2-1 loss to Skonto FC.
As of November 2013, Koļinko has 88 caps for Latvia national football team, having made his international debut against Estonia on 9 July 1997 at the age of 22. He became the first-choice keeper in 1999 after the retirement of Oļegs Karavajevs. Koļinko was Latvia's first-choice keeper for almost ten years. He was the starting goalkeeper for Latvia at Euro 2004, playing 90 minutes in all matches and keeping a clean sheet against Germany in the second match of the group stages. From 2011 to 2013 Koļinko was temporarily excluded from the national squad with Andris Vaņins filling the first keeper's spot and Deniss Romanovs, Pāvels Doroševs or Germans Māliņš serving as the back-up choice. On 10 September 2013, at the age of 38, Koļinko made his national team comeback, playing a full match away in the 2014 FIFA World Cup qualifiers against Greece. He made a handful of great saves, conceding one goal to the locals. Koļinko played his second international match since returning to the national team on 15 October 2013, helping Latvia secure a point in the last match of the 2014 FIFA World Cup qualifiers, playing a 2-2 draw against Slovakia. All in all Koļinko played 94 international matches for Latvia over the period from 1997 to 2015. He played his last international match on 31 March 2015, as Latvia drew 1-1 against Ukraine in a friendly match.
In July 2015 Koļinko was appointed as the manager of Spartaks Jūrmala after the departure of Roman Pylypchuk. Failing to impress, he was replaced by Oleg Kubarev in December 2015. Since then Koļinko has remained at the club, working as the assistant manager and goalkeeping coach of the first team.Skonto Riga
Latvian Higher League champion (5): 1996, 1997, 1998, 1999, 2000
Latvian Cup winner (3): 1997, 1998, 2000
Baltic League champion (1): 2009-10
Latvian Higher League best goalkeeper (3): 1997, 1999, 2000
Latvian Footballer of the Year (2): 2006, 2014
Latvian Higher League champion (1): 2016