Steerable needles capable of taking curvilinear trajectories through tissue enable the ability to avoid anatomical obstacles and home in on targets. However, steerable needle designs that are pushed into tissue from their base struggle to take tight curvatures without damaging tissue due to the needle cutting laterally through tissue. In this work, we propose a new type of steerable needle that can take much tighter curvatures safely. This needle pulls itself through tissue via a screw tip, with rotation imparted at its base. The needle is steered by applying a magnetic field, and thus a magnetic steering torque, to a magnetic dipole at the needle's tip via an external permanent magnet. Our design leverages extremely soft tubing for its shaft, which enables the shaft to have low bending stiffness and impart low forces on surrounding tissues and enabling high curvatures---approximately 26mm radius of curvature in this work. This potentially unlocks clinical applications such as targeted therapy in brain tissue, e.g., stereotactic ablation of the hippocampus and the amygdala for epilepsy treatment. We demonstrate our needle's ability to more closely conform to these brain structures' complex geometries in gelatin, as well as the ability to steer in ex vivo brain tissue.