Anglo first referred to the Angles, the Germanic peoples who invaded Britain around 450. Angli (Angles) was used in Latin as early as the 6th century. Aethelbert was called rex Anglorum (king of the Angles) in 601. And later in that century the country was sometimes called Angli or Anglia (this eventually became England, but not till much later).

Sources: The Cambridge Encyclopedia or the English Language, and The Stories of English by David Crystal

According to the OED Sino- comes from the late Latin "Sinæ " in reference to the Chinese (from the Arabic "Sin" for the same) and the prefix wasn't in use until the nineteenth century, whereas Anglo- is post-classical Latin that was first used in the sixteenth century but didn't pick up until the eighteenth.