Robotic telesurgical systems are one of the most complex medical cyber-physical systems on the market, and have been used in over 1.75 million procedures during the last decade. Despite significant improvements in design of robotic surgical systems through the years, there have been ongoing occurrences of safety incidents during procedures that negatively impact patients. This paper presents an approach for systems-theoretic safety assessment of robotic telesurgical systems using software-implemented fault-injection. We used a systemstheoretic hazard analysis technique (STPA) to identify the potential safety hazard scenarios and their contributing causes in RAVEN II robot, an open-source robotic surgical platform. We integrated the robot control software with a softwareimplemented fault-injection engine which measures the resilience of the system to the identified safety hazard scenarios by automatically inserting faults into different parts of the robot control software. Representative hazard scenarios from real robotic surgery incidents reported to the U.S. Food and Drug Administration (FDA) MAUDE database were used to demonstrate the feasibility of the proposed approach for safety-based design of robotic telesurgical systems.