A spouse can get temporary residency in Argentina through the following visa category:
23 “in fine” Visa or Temporary Family Reunification- It is applicable for the family of the expat, which includes spouse, parent or unmarried children under 18 years of age or children with disabilities of a temporary resident in Argentina. It is usually given when the term of stay is shorter like up to one year.
For expats intending to reside in Argentina permanently, you need to apply for Permanent Residency through 22 Visa.
22 Visa- 22 Visa- It is applicable for the family of an expat, who wish to settle in Argentina permanently. The applicants can be spouse, parent or children under 18 years of age or older, children with disabilities of a temporary or permanent resident in Argentina. Getting permanent residency in Argentina is a bit tedious, so you have to be prepared for frequent trips to the immigration office.
Once all the documents are done, you need to make an appointment with the local immigration office. After all your documents are submitted along with the registration fees, you will receive a temporary Certificate for Residence. This certificate gives you the permission to study or work, get a house and leave or reenter the country. It’s a temporary document that is good for six months, until the government processes the request for permanent residency permit. The process can take anywhere from a couple of months to a year. Sometimes, you may be called to the immigration office for an interview to ensure that you didn’t enter into a fake marriage for visa purposes.
When you receive the permanent residency permit, next you need to start the process for applying a DNI. It can be issued on a temporary basis for 60 days or on permanent basis depending on the residency permit. It is issued by the National Direction of Migration.
Source : http://www.migraciones.gov.ar/accesibleingles/?mercosur_temporaria