Robotic surgical systems are among the most complex medical cyber-physical systems on the market. Despite significant improvements in design of those systems through the years, there have been ongoing occurrences of safety incidents that negatively impact patients during procedures. This paper presents an approach for systems-theoretic safety assessment of robotic telesurgical systems using software-implemented fault injection. We used a systems-theoretic hazard analysis technique (STPA) to identify the potential safety hazard scenarios and their contributing causes in RAVEN II, an open-source telerobotic surgical platform. We integrated the robot control software with a software-implemented fault injection engine that measures the resilience of system to the identified hazard scenarios by automatically inserting faults into different parts of the 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.