Why not just buy a throw away? No phone, no records of who was called, or originated the call.
Cell phone calls go to a cell tower which decrypts the digital sound and sends it off unencrypted to a centralized digital network to be routed. The records of who called whom from what cell are available, and if there's a court order, a copy of the sound. National security agencies intercept phone traffic and use computers to perform voice fingerprints and generate transcripts that can be scanned for keyword combinations. Buying throw aways doesn't insure they can't figure out who someone is, just makes it a little harder, and a little more incriminating that they're up to something. It's technically possible to set up an encrypted and anonymous cell phone system using specially modified cell phones however if it became popular the Feds would likely make it illegal.