ICC have no power, it is basically just a promise that countries can chose to sign or not. Russia and USA among many other countries have not signed it.
And even if your country has signed the promise, you can get away with not upholding said promise.
South Africa who's a signatory member of ICC chose to ignore an arrest warrant on the president of Sudan in 2015.
As their website says, they are an intergovernmental organisation designed to try individuals for genocide, other war crimes, crimes against humanity, and aggression.
They have the power to ask signatory nations for the arrest of suspects, and to try and (where appropriate) sentence those suspects.