The term "genocide" originated during WWII by Polish lawyer Raphael Lemkin and was adopted officially in 1948 by the United Nations in the Genocide Convention (UN).
It is important to distinguish between the specific crime of genocide outlined above and the series of crimes known more broadly as war crimes. Consult the resource below:
War Crimes: A Primer from the Congressional Research Service
The International Criminal Court (ICC) may be the place to bring accusations of genocide, but the accused must be a member of the ICC (some nations, like the US and Myanmar/Burma, are not), or the UN Security Council can refer the case to the ICC. The UN's World Court (also known as the International Court of Justice or ICJ), can hear cases relating to violations of the Genocide Convention. The US has other means to bring scrutiny and prosecution of genocide:
the US Criminal Code defines genocide and provides the means to prosecute and punish perpetrators
the Office of Global Criminal Justice coordinates US cooperation with international agencies
the War Crimes Rewards Program offers a reward to anyone who provides information that leads to legal action for perpetrators of genocide or other crimes
NPR recently reviewed the history of bringing war criminals to justice, including those charged with genocide: "From Nuremberg to Darfur, history has seen some war criminals brought to trial"