Is the correct description of a person from Argentina Argentinian or Argentine?

Argentinian

While 'Argentinian' is often used in the UK, and can be found in various dictionaries, it belongs to that classification of Words that has become accepted through usage, not because it is -or has ever been- entirely correct. Official United Nations documents and US Government official translations use 'Argentine'. 'Argentinian' may be used, but so may many slang and argot Words. Personal style and preference, as well as nationality will dictate which of the two Words a person uses. Anyone wishing to achieve the highest level of correct usage will use the Word Argentine. For what it's worth, people from Argentina call themselves Argentinos or Argentinas (depending on gender), and not ArgentiniOS, or Argentinias.