If you are married to Argentinian Citizen, you have full rights to apply for the permanent residency. The application process is same with other cases, just need to demonstrate the marriage certificate during the process. Here is the list of documents you have to submit.
1.- Identity Documents(International Passport)
2.- Birth Certificate Apostilled and Translated
3.- Argentine Criminal Record Certificate issued by the National Registry of Recidivism or the Federal Police (Only required for those over 16 years of age).
4.- Certificate that reliably certifies that there are no previous convictions or pending criminal proceedings, issued by the competent authorities of the countries where you have resided for a period of more than ONE (1) year, during the course of the last THREE (3) years, (Only required to over 16 years).
5.- Stamp of entry to the country stamped on the travel document.
6.- Certificate of Address or a bill from a public service in your name (ABL, electricity, water or gas).
7.- Marriage certificate and the DNI Permanente or Passport of your Argentinian Spouse
If you are married to an Argentine citizen born in Argentina, (not naturalized citizen), are also eligible for simplified citizenship which means you don’t have to wait two years to apply for citizenship.