In this paper, with the goal of enhancing the minimally invasive spinal fixation procedure in osteoporotic patients, we propose a first-of-its-kind image-guided robotic framework for performing an autonomous and patient-specific procedure using a unique concentric tube steerable drilling robot (CT-SDR). Particularly, leveraging a CT-SDR, we introduce the concept of J-shape drilling based on a pre-operative trajectory planned in CT scan of a patient followed by appropriate calibration, registration, and navigation steps to safely execute this trajectory in real-time using our unique robotic setup. To thoroughly evaluate the performance of our framework, we performed several experiments on two different vertebral phantoms designed based on CT scan of real patients.