As quantum computing advances, quantum circuit simulators serve as critical tools to bridge the current gap caused by limited quantum hardware availability. These simulators are typically deployed on cloud platforms, where users submit proprietary circuit designs for simulation. In this work, we demonstrate a novel timing side-channel attack targeting cloud- based quantum simulators. A co-located malicious process can observe fine-grained execution timing patterns to extract sensitive information about concurrently running quantum circuits. We systematically analyze simulator behavior using the QASMBench benchmark suite, profiling timing and memory characteristics across various circuit executions. Our experimental results show that timing profiles exhibit circuit-dependent patterns that can be effectively classified using pattern recognition techniques, enabling the adversary to infer circuit identities and compromise user confidentiality. We were able to achieve 88% to 99.9% identification rate of quantum circuits based on different datasets. This work highlights previously unexplored security risks in quantum simulation environments and calls for stronger isolation mechanisms to protect user workloads