Drozdov won his first national championship as a skip in 2009. He has represented Russia in six European Curling Championships. In 2007, he placed 14th playing third for Alexander Kirikov. In 2008, he placed 15th as the skip of the Russian team. In 2009, he placed 12th as the team's skip. Drozdov also skipped the Russian team at the 2009 World Junior Curling Championships, placing 7th. In 2010, he placed 9th as skip. In 2011 he played second for Alexey Tselousov and the team had an 11th-place finish. At the 2012 European Curling Championships, Drozdov lead Russia to their best finish, 5th, qualifying for the World Championships for the first time.