The high-Q harmonic oscillator mode of a Josephson junction can be used as a novel probe of spurious two-level systems (TLSs) inside the amorphous oxide tunnel barriers of the junction. In particular, we show that spectroscopic transmission measurements of the junction resonator mode can reveal how the coupling magnitude between the junction and the TLSs varies with an external magnetic field applied in the plane of the tunnel barrier. The proposed experiments offer the possibility of clearly resolving the underlying coupling mechanism for these spurious TLSs, an important decoherence source limiting the quality of superconducting quantum devices.Superconducting quantum circuits have been intensively tested in various regimes in the past few years, from superconducting qubits demonstrating long coherence times, to superconducting transmission line cavities coherently coupled to a Single Cooper Pair box [1,2,3,4,5,6]. Such circuits are extremely sensitive to very small quanta and defect states, and hence have the ability to detect individual microwave photons, charged quasiparticles, as well as spurious TLSs within or near Josephson junction tunnel barriers [7,8,9,10,11]. In recent experiments [10,11], TLSs were identified through spectroscopic measurements of a superconducting phase qubit appearing as 'gaps" or "splittings" in the energy spectrum.The TLS defects can be an unwanted source of decoherence for superconducting quantum bits. The lowfrequency noise, which has been shown to be a serious source of decoherence for superconducting qubits [10,11,12,13,14], is very probably induced by such amorphous fluctuators inside or near Josephson junctions [15,16]. Understanding the origin of these spurious TLSs, their coherent quantum behavior, and their connection to ubiquitous 1/f noise is hence a challenge that will be crucial to the future of superconducting quantum devices. The behavior of a distribution of these TLSs were studied theoretically in [17,18,19]. Recently, it was proposed that TLSs can be viewed as qubits themselves [20], given their relatively long coherence times. However, the microscopic origin and the coupling mechanism between the TLSs and the junction remains unresolved. Generally considered to be connected to the amorphous nature of the tunnel barrier [21], movement of unrestrained atoms or charges may lead to a number of possible coupling mechanisms. As originally proposed in Ref. [11], fluctuations of the TLS could lead to variations of the junction critical current. Another possibility, requires that the TLSs have fluctuating dipole moments which couple to the electric field found within the junction tunnel barrier [10].Here, we present a scheme that can resolve a variety of properties of the TLSs and distinguish between these two suggested coupling mechanisms through the use of an applied magnetic field. Consider a Josephson junction resonator operating as a high-Q, nonlinear cavity mode [22], coupling to a TLS through its canonical phase (or momentum) operator. This forms a cavity QED sys...