Anisimov was drafted 54th overall in the 2006 NHL Entry Draft by the New York Rangers. He took part in the 2007 World Junior Championship with the Russian National Team, collecting 2 goals and one assist in 6 games. Anisimov made a brief National Hockey League debut in 2008-09, meanwhile enjoying a solid campaign in the AHL with the Wolf Pack, scoring 37 goals and 44 assists in 80 games. In 2009-10, he became a regular on the Rangers squad. His first NHL goal came on October 11th 2009 in a 3-0 win over the Anaheim Ducks.