Private Prison Information Act of 2021 This bill specifies that a record related to a nonfederal prison, correctional, or detention facility must be considered a federal agency record for purposes of the Freedom of Information Act (FOIA). A nonfederal prison, correctional, or detention facility must disclose information under FOIA unless the information is exempt from disclosure or the disclosure is prohibited by law. The term nonfederal prison, correctional, or detention facility means (1) a private prison, correctional, or detention facility; or (2) a state or local prison, jail, or other correctional or detention facility.