Sten was born December 3, 1908, in Kiev, then part of the Russian Empire. There are other conflicting dates of birth: 1910 and 1906 from self-written dates in application forms from college. Her mother, Alexandra, listed Anna's birthdate as October 29, 1906, upon her arrival in the United States, although some of the discrepancies may be owing from the switch from the Julian calendar (still used in the Russian Empire up to 1918) to the Gregorian calendar. According to the official biography, her father was born into a Cossack family, worked as a theater artist and producer. Her mother was a Swede by birth and was a ballerina. In Kiev in the middle of the 1920s she married entertainer and variety actor Boris Sten (né Bernstein), and took his stage name as her own.