Edited per remark by @phoog about the meaning of complaint.
I'm filing a complaint with his Editor-in-Chief. He did record the
lengthy call, and I'd like to know if I have a right to obtain a copy
of that recording.
You might have a right under principles of equity to obtain a copy. First, because you took part in the interview. And second, because the plagiarized work is yours. It is otherwise unlikely that a statute entitles you to get a copy of that recording.
In the event that you file a lawsuit, the editor/reporter is unlikely to succeed in his refusal to produce a copy. But you would have to request that through a subpoena (and possibly a subsequent motion to compel discovery) as part of the discovery process of your lawsuit.