This paper proposes a novel framework for identifying an agent's risk aversion using interactive questioning. We assume that the agent's risk aversion is characterized by a distortion risk measure chosen from a finite set of candidates. We show that asking the agent to choose from a finite set of random costs, which may depend on their previous answers, is an effective means of identifying the agent's risk aversion. Specifically, we prove that the agent's risk aversion can be identified as the number of questions tends to infinity, and the questions are randomly designed. We also develop an algorithm for designing optimal questions and provide empirical evidence that our method learns risk aversion significantly faster than randomly designed questions in a simulated environment. Our framework has important applications in robo-advising and provides a new approach for identifying an agent's risk preferences.