Federal, state, and local prisons and jails include chaplains to varying degrees. All federal prisons, including ICE detention centers, have chaplains.
Training & Qualifications
To work as a chaplain in a federal prison, you also have to be endorsed by a religious group. There is no standard list of endorsers for the Federal Bureau of Prisons as explained here. For the most part the same person or office handles all federal endorsements in most traditions. If you are having difficulty identifying the endorser in your tradition for the Federal Bureau of Prisons, try contacting the military or VA endorser.
Federal Bureau of Prisons: Chaplain (Job Series Number: 0060)