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Composites printed using material extrusion additive manufacturing (AM) typically exhibit alignment of high- aspect-ratio reinforcements parallel to the print direction. This alignment leads to highly anisotropic stiffness, strength, and transport properties. In many cases, it would be desirable to increase mechanical and transport properties transverse to the print direction, for example, in 3D-printed heat sinks or heat exchangers where heat must be moved efficiently between printed roads or layers. Rotational direct ink writing (RDIW), where the deposition nozzle simultaneously rotates and translates during deposition, provides a method to reorient fibers transverse to the print direction during the printing process. In the present work, carbon fiber-reinforced epoxy composites were printed by RDIW with a range of nozzle rotation rates and the in-plane and through-thickness thermal conductivity was measured. In addition, the orientation of carbon fiber (CF) in the composites was measured using optical microscopy and image analysis, from which second-order fiber orientation tensors were calculated. These results showed that the orientation of CF became less anisotropic as nozzle rotation rate increased, leading to increased through-thickness thermal conductivity, which increased by 40% at the highest rotation rate. The orientation tensors also showed that RDIW was more effective at reorienting fibers within the in-plane transverse direction compared to the through-thickness transverse direction. The results presented here demonstrate that a current weakness of material extrusion AM composites—poor thermal conductivity in the through-thickness direction—can be significantly improved with RDIW.