Alexander Schapiro was born in 1882 or 1883 in Rostov-on-Don in southern Russia. He grew up in Constantinople because his father Moses, a member of the secret revolutionary organization "Narodnaya Volya", which assassinated Tsar Alexander II in 1881, was forced to flee the Russian Empire. There, he attended the French school. Schapiro grew up speaking Yiddish, Russian, French, and Turkish, and would later learn German and English. In the mid-1890s, Moses Schapiro converted to anarchism and by age eleven Alexander Schapiro started studying the works of anarchist theorists like Peter Kropotkin, Jean Grave and Élisée Reclus. In the late 1890s, the Schapiro family moved to London and came into contact with the milieu of Jewish anarchists behind the journal "Arbeyter Fraynd". After finishing school, Schapiro moved to Sofia, Bulgaria in 1899 to study mathematics and physics.