A non-contact laser polishing method for additively manufactured polymer components with complex three-dimensional geometries is presented, employing a 6-axis robotic system. Robot-guided sample orientation, a quasi-top-hat scanning strategy, and closed-loop temperature control are combined to address curved geometries. On Selective Laser Sintering (SLS)-manufactured Polyamide 12 (PA12) tensile samples with three build orientations and two thicknesses, laser polishing yields up to a 15% increase in tensile strength (Rm) and a 50% increase in elongation at break (A). For 45°-built 5 mm samples, Rm increases from 31.53 MPa to 36.33 MPa and A from 6.52% to 9.8%, approaching the tensile strength reported for optimally oriented SLS-printed PA12 Smooth samples of the same grade. For convex–concave PA12 demonstrators, areal roughness (Sa) on convex surfaces is reduced from 33.6 µm to 2.7 µm (approximately 92%) and the high-pass-filtered micro-roughness (Sa_HP) on concave surfaces by 98.2% to 0.15 µm. For Fused Deposition Modeling (FDM)-printed Polyaryletherketone (PAEK) samples, Sa is reduced from 28.35 µm to 4.1 µm and Sa_HP from 15.98 µm to 0.23 µm (98.6%), despite the high melting temperature and anisotropic raster topography. These results demonstrate that robotic laser polishing constitutes a viable post-processing approach for functionally demanding polymer applications.