Additive manufacturing (AM) has opened new frontiers in precision medicine, giving the possibility of fabricating patient‐customized scaffolds to replace damaged tissues. In particular, bone tissue engineering (BTE) has benefited the most from the introduction of AM. In contrast, the impelling environmental issues are moving all the industrial sectors toward a sustainable development, avoiding the use of nonrenewable resources. Since thermoplastic polymers, such as poly(lactic acid) (PLA) and polycaprolactone (PCL), are massively used in the biomedical field, the primary objective of this study is to encourage the use of biodegradable and compostable materials also in BTE. Focusing on poly(3‐hydroxybutyrate‐co‐3‐hydroxyhexanoate) (PHBH), an eco‐friendly material with good biocompatibility and biodegradability, reinforced with cellulose nanocrystals (CNCs), 3D‐printed scaffolds through fused filament fabrication (FFF) are realized. Since vascularization is mandatory for bone regeneration processes and for a successful scaffold integration, the angiogenic potential of different PHBH–CNC formulations in vitro is tested, evaluating the colonization of the scaffolds by endothelial cells, and in ovo with the chorioallantoic membrane (CAM) assay. The final goal is to define the best geometry of the scaffold and PHBH–CNC composition that can trigger vascularization in BTE applications, with the ultimate aim of giving greater guarantees of osseointegration.