Hi Tyler,
Sorry we don't have a way inside AFNI to write DICOM files, but this has come up a couple times before. These links might give you some way to do this. I've tried one of ImageJ's DICOM plug-ins to do this, and it's possible to replace the data of a similar set of DICOM files with processed data using file_tool, but these things are full of difficulties especially for regular use.
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afni.nimh.nih.gov]