Slender continuum robots are uniquely placed to address inspection and intervention tasks in difficult-to-access environments. Tasks such as minimally invasive surgery and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> maintenance of complex machinery require dexterous robots with accurate motion control, and benefit from instruments with small diameters and large internal passages for services. Intrinsic proprioception, or built-in position sensory feedback, has been described in prior work on continuum and soft robots but seldom employed for motion closed-loop control. In this research article, we present a novel tubular resistive stretch sensor with ionic liquid conductors to enable closed-loop position control of low-cost, 3-D printed continuum robots. We describe a methodology for sensor characterization and calibration drawing from a model of their behavior under strain, allowing us to apply four stretch sensors as proprioceptive feedback for motion control of a four-axis slender continuum manipulator. We demonstrate a substantial (approximately 65%) improvement in position control accuracy and repeatability over open-loop methods and show a promising step toward low-cost, scalable position feedback for slender continuum robots.