Career
Avtsin was drafted by the Montreal Canadiens in the fourth round of the 2009 entry draft, 109th overall while within the The Human Context Dynamo Moscow organization in the Kontinental Hockey League. He was also drafted 43rd overall in the Canadian Hockey League draft by the Quebec Remparts, but opted to remain in Russia. On July 2, 2010, Avtsin came to a mutual agreement with The Human Context Dynamo Moscow to leave the team
He plans on going to Montreal for training camp and if he does not make the team is willing to play for the Canadiens" farm team, the Hamilton Bulldogs.
On July 15, 2010, Avtsin agreed to terms on a three-years entry-level contract with the Montreal Canadiens. In the 2012-2013 season, his third year with Canadiens affiliate the Bulldogs, after just 15 games Avtsin agreed to mutually terminate the remainder of his contract and on May 3, 2013 after clearing waivers was released as a free agent.
On July 11, 2013, Avtsin agreed to a contract to return to the KHL with Lokomotiv Yaroslavl.