Low background rare-event physics experiments and ultrasensitive radiation detectors require materials of the utmost radiopurity to meet their sensitivity goals. Polymers are important materials used extensively in these detectors in a variety of roles, including as insulators and structural supports. Oftentimes, specialized polymer parts are co-located with the active detection target, necessitating their radioactive background contribution to be as low as possible. Additive manufacturing, or 3D-printing, has been discussed as a possible means to fabricate complex parts of low mass for niche applications but requires vetting for radiopurity. This work investigated several different polymer feedstocks, including polyphenylene sulfide (PPS), polyvinylidene fluoride (PVDF), polyetherimide (PEI), and utilized a fused deposition modeling printer to fabricate parts. Both simple and complex parts were fabricated and assayed along with the starting filament feedstocks. Results indicate that both simple and complex parts can be produced with little-to-no radioactivity added, with the best polymer showing levels for Th-232 and U-238 at single digit parts-per-trillion levels (ca. 100 microBq/kg).