There is no filing requirement in the constitution. The only law that potentially applies is the presidential record's act, which requires records of official acts to be turned over to the National Archives at the end of a president's term. However, there is no enforcement mechanism in that law that would retroactively invalidate an action if the underlying record is not turned over (and even if there were, it would likely be unconstitutional). So as long as the pardon is genuine and issued by the president while in office, there's a strong argument that he has no obligation to make it public. Democrats Are Worried Trump Will Secretly Pardon People. Can He Do That?