Scaling up superconducting quantum processors remains a central challenge for realizing fault-tolerant quantum computation. Although distributed architectures based on optical photons offer a promising route to scalability, they require an efficient microwave-to-optical quantum transducer that operates at cryogenic temperatures. Existing approaches typically rely on strong optical pumping, which induces undesirable heating and degrades single-photon coherence. Here, we propose a microwave-to-optical quantum transducer based on resonant scattering at a single color center embedded in a diamond optomechanical resonator. We show that strong coupling between the color center and the optical cavity enables coherent conversion at extremely weak pump powers on the order of 10 pW. The proposed scheme enables remote entanglement generation at a kilohertz-scale rate with a fidelity exceeding 0.9, demonstrating a viable pathway toward ultra-weak-pump and high-efficiency quantum transducers based on a solid-state defect.