She was the first woman to be nominated for the Court by a democratic government in Argentina, and caused some controversy upon declaring herself an atheist and a supporter of legal abortion.

After the return of democratic rule, on 7 June 1984, she was appointed judge in a criminal court in Buenos Aires.

In June 2001 she was appointed ad litem judge at the International Criminal Tribunal for the former Yugoslavia (ICTY).

Argibay was one of the first Justices who entered the Argentine Supreme Court when President Néstor Kirchner started to push for its renewal.

When the nomination was made public, a number of conservative voices criticized her for her atheism and her stance on abortion; a Catholic organization complained that Argibay, who is single and childless, was "not representative of Argentine women."