Textile-based compression devices are widely used in fields such as healthcare, astronautics, cosmetics, defense, and more. While traditional compression garments are only able to apply passive pressure on the body, there have been some efforts to integrate smart materials such as shape memory alloys (SMAs) to make compression garments active and controllable. However, despite the advances in this field, accurate control of applied pressure on the body due remains a challenge due to vast population-scale anthropometric variability and intra-subjects variability in tissue softness, even if the actuators themselves are fully characterized. In this study, we begin to address these challenges by developing a novel size-adjustable SMA-based smart tourniquet capable of producing a controllable pressure for circumferential applications. The developed prototype was tested on an inflatable pressure cuff wrapped around a rigid cylinder. The thermal activation of SMA coils was achieved through Joule heating, and a microcontroller and a programmable power supply are used to provide the input signal. To control the compression force, a closed-loop PID controller was implemented, and the performance of the system was evaluated in 5 different testing conditions for variable and cyclic compression levels. The experiments showed that the controlled system could follow the desired control pressure reference with a steady-state of 1 mmHg. The compression tourniquet is able to produce more than 33 mmHg with an average actuation rate of 0.19 mmHg/s. This is the first demonstration of accurate closed-loop control of an SMA-incorporated compression technology to the best of our knowledge. This paper enables new, dynamic systems with controllable activation and low-effort donning and doffing, with applications ranging from healthcare solutions to advanced spacesuit design.