In the clinical setting of bone fracture healing, hardware removal often causes localized microtrauma and residual screw holes may act as stress risers to place the patient at a risk of refracture. To address this noted issue, this study proposed to develop a biologically mimicking and mechanically self-actuated nanofibrous screw-like scaffold/implant for potential in situ bone regeneration. By incorporating nano-hydroxyapatite (HAp) into a shape memory copolymer poly(d,l-lactide-co-trimethylene carbonate) (PLMC) via co-electrospinning, composite nanofibers of HAp/PLMC with various HAp proportions (1, 2 and 3 wt%) were successfully generated. Morphological, thermal and mechanical properties as well as the shape memory effect of the resultant HAp/PLMC nanofibers were characterized using a variety of techniques. Thereafter, osteoblasts isolated from rat calvarial were cultured on the fibrous HAp/PLMC scaffold to assess its suitability for bone regeneration in vitro. We found that agglomerates gradually appeared on the fiber surface with increasing HAp loading fraction. The switching temperature for actuating shape recovery Ts (i.e., glass transition temperature Tg) of the fibrous HAp/PLMC was readily modulated to fall between 43.5 and 51.3 °C by varying the HAp loadings. Excellent shape memory properties were achieved for the HAp/PLMC composite nanofibers with a shape recovery ratio of Rr > 99% and shape fixity ratio of Rf > 99%, and the shape recovery force of the HAp/PLMC nanofibers was also strengthened compared to that of the HAp-free PLMC nanofibers. Moreover, we demonstrated that the engineered screw-like HAp/PLMC scaffold/implant (ϕ = 5 mm) was able to return from a slender bar to its original stumpy shape in a time frame of merely 8 s at 48 °C. Biological assay results corroborated that the incorporation of HAp to PLMC nanofibers significantly enhanced the alkaline phosphatase secretion as well as mineral deposition in bone formation. These attractive results warrant further investigation in vivo on the feasibility of applying the biomimicking nanofibrous HAp/PLMC scaffold with shape memory effect for bone screw hole healing.