Tailor-made polymers are needed to fully exploit the possibilities of additive manufacturing, constructing complex, and functional devices in areas such as bioelectronics. In this paper, the synthesis of a conducting and biocompatible graft copolymer which can be 3D printed using direct melting extrusion methods is shown. For this purpose, graft copolymers composed by conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT) and a biocompatible polymer polylactide (PLA) are designed. The PEDOT-g-PLA copolymers are synthesized by chemical oxidative polymerization between 3,4-ethylenedioxythiophene and PLA macromonomers. PEDOT-g-PLA copolymers with different compositions are obtained and fully characterized. The rheological characterization indicates that copolymers containing below 20 wt% of PEDOT show the right complex viscosity values suitable for direct ink writing (DIW). The 3D printing tests using the DIW methodology allows printing different parts with different shapes with high resolution (200 µm). The conductive and biocompatible printed patterns of PEDOT-g-PLA show excellent cell growth and maturation of neonatal cardiac myocytes cocultured with fibroblasts.