Social robots serve as autonomous systems for performing social behaviors and assuming social roles. However, there is a lack of research focusing on the specific measurement of facial trustworthiness toward anthropomorphic robots, particularly during initial interactions. To address this research gap, a hybrid deep convolution approach was employed in this study, involving a crowdsourcing platform for data collection and deep convolution and factor analysis for data processing. The goal was to develop a scale, called Facial Anthropomorphic Trustworthiness towards Social Robots (FATSR-17), to measure the trustworthiness of a robot’s facial appearance. The final measurement scale comprised four dimensions, “ethics concern”, “capability”, “positive affect”, and “anthropomorphism”, consisting of 17 items. An iterative examination and a refinement process were conducted to ensure the scale’s reliability and validity. The study contributes to the field of robot design by providing designers with a structured toolkit to create robots that appear trustworthy to users.