Quantum compilers play a crucial role in quantum computing by converting these algorithmic quantum circuits into forms compatible with specific quantum computer hardware. However, untrusted quantum compilers present considerable risks, including the potential theft of quantum circuit intellectual property (IP) and compromise of the functionality (e.g. Trojan insertion). Quantum circuit obfuscation techniques protect quantum IP by transforming a quantum circuit into a key-dependent version before compilation and restoring the compiled circuit's functionality with the correct key. This prevents the untrusted compiler from knowing the circuit's original functionality. Existing quantum circuit obfuscation techniques focus on inserting key qubits to control key gates. One added key gate can represent at most one Boolean key bit. In this paper, we propose OPAQUE, a phase-based quantum circuit obfuscation approach where we use the angle of rotation gates as the secret keys. The rotation angle is a continuous value, which makes it possible to represent multiple key bits. Moreover, phase gates are usually implemented as virtual gates in quantum hardware, diminishing their cost and impact on accuracy.