Radio signal classification plays a pivotal role in identifying the modulation scheme used in received radio signals, which is essential for demodulation and proper interpretation of the transmitted information. Researchers have underscored the high susceptibility of ML algorithms for radio signal classification to adversarial attacks. Such vulnerability could result in severe consequences, including misinterpretation of critical messages, interception of classified information, or disruption of communication channels. Recent advancements in quantum computing have revolutionized theories and implementations of computation, bringing the unprecedented development of Quantum Machine Learning (QML). It is shown that quantum variational classifiers (QVCs) provide notably enhanced robustness against classical adversarial attacks in image classification. However, no research has yet explored whether QML can similarly mitigate adversarial threats in the context of radio signal classification. This work applies QVCs to radio signal classification and studies their robustness to various adversarial attacks. We also propose the novel application of the approximate amplitude encoding (AAE) technique to encode radio signal data efficiently. Our extensive simulation results present that attacks generated on QVCs transfer well to CNN models, indicating that these adversarial examples can fool neural networks that they are not explicitly designed to attack. However, the converse is not true. QVCs primarily resist the attacks generated on CNNs. Overall, with comprehensive simulations, our results shed new light on the growing field of QML by bridging knowledge gaps in QAML in radio signal classification and uncovering the advantages of applying QML methods in practical applications.