Which century is the primary historical period of the original Assassin's Creed?

The original Assassin's Creed is primarily set in the 12th century.

Its historical sections take place during the Third Crusade, chiefly in 1191. Altaïr Ibn-La'Ahad travels among the cities of Jerusalem, Acre, and Damascus while carrying out missions connected to the conflict between the Assassins and Templars.

The year 1191 places the game near the end of the Third Crusade, which began in 1189 after the capture of Jerusalem by Saladin's forces in 1187. The game uses real cities and historical figures, but its secret organizations, conspiracies, and supernatural artifacts are fictionalized for the series' narrative.

The modern-day sections occur in a different period and follow Desmond Miles. That split can cause confusion when describing the game's date, but the primary playable historical setting is firmly medieval rather than Renaissance or ancient.