But more than a year later, SNAP said the church has not done enough to prosecute the higher-level officials in cases of alleged cover-ups.
"There has been much talk of 'reforms' and 'zero tolerance' policies by church officials over the past few years," the complaint says. "As recent commissions of inquiry and grand jury findings discussed herein demonstrate, sexual violence is still being committed within the church with impunity and the priest-shifting and cover-ups are still happening, also with impunity."
The International Criminal Court is meant to try cases involving "the most serious crimes of international concern, namely genocide, crimes against humanity and war crimes," according to the court's website.
A spokesperson for the church declined to comment on the complaint for this report.
ABC News' Phoebe Natanson and The Associated Press contributed to this report.