He was the son of Desiderio Alberto Arnaz y Alberni (1857–1929), a medical doctor (and grandson of Manuel Arnaz, a mayor of Santiago de Cuba in 1869), and Rosa Alberni y Portuondo (1870–unknown), a member of the Cuban nobility and the great-granddaughter of a mayor of Santiago de Cuba, José Joaquín Portuondo y Rizo, 1st Conde de Santa Inés (1762–1824).
[citation needed] Arnaz was the youngest mayor of Santiago de Cuba (1923–1932).
He was elected to the Cuban House of Representatives in November 1932 for the Oriente Province.
When president Gerardo Machado was overthrown in August 1933, Rep. Arnaz was arrested and jailed.
He is entombed above President Machado at Caballero Rivero Woodlawn North Park Cemetery and Mausoleum.