Social touch forms an important aspect of the human non-verbal communication repertoire, but is often overlooked in human–robot interaction. In this study, we investigated whether robot-initiated touches can induce physiological, emotional, and behavioral responses similar to those reported for human touches. Thirty-nine participants were invited to watch a scary movie together with a robot that spoke soothing words. In the Touch condition, these words were accompanied by a touch on the shoulder. We hypothesized that this touch—as compared with no touch—could (H1) attenuate physiological [heart rate (variability), skin conductance, cortisol, and respiration rate] and subjective stress responses that were caused by the movie. Moreover, we expected that a touch could (H2) decrease aversion toward the movie, (H3) increase positive perceptions of the robot (e.g., its appearance and one’s attitude toward it), and (H4) increase compliance to the robot’s request to make a monetary donation. Although the movie did increase arousal as intended, none of the hypotheses could be confirmed. Our findings suggest that merely simulating a human touching action with the robot’s limbs is insufficient to elicit physiological, emotional, and behavioral responses in this specific context and with this amount of participants. To inform future research on the opportunities and limitations of robot-initiated touch, we reflect on our methodology and identify dimensions that may play a role in physical human–robot interactions: e.g., the robot’s touching behavior, its appearance and behavior, the user’s personality, the body location where the touch is applied, and the (social) context of the interaction. Social touch can only become an integral and effective part of a robot’s non-verbal communication repertoire, when we better understand if, and under which boundary conditions such touches can elicit responses in humans.