This paper introduces a new type of soft continuum robot, called SCoReS, which is capable of self-controlling continuously its curvature at the segment level; in contrast to previous designs which either require external forces or machine elements, or whose variable curvature capabilities are discrete -- depending on the number of locking mechanisms and segments. The ability to have a variable curvature, whose control is continuous and independent from external factors, makes a soft continuum robot more adaptive in constrained environments, similar to what is observed in nature in the elephant's trunk or ostrich's neck for instance which exhibit multiple curvatures. To this end, our soft continuum robot enables reconfigurable variable curvatures utilizing a variable stiffness growing spine based on micro-particle granular jamming for the first time. We detail the design of the proposed robot, presenting its modeling through beam theory and FEA simulation -- which is validated through experiments. The robot's versatile bending profiles are then explored in experiments and an application to grasp fruits at different configurations is demonstrated.