We demonstrate a total charge parity measurement by detecting the radio frequency signal that is reflected by a lumped element resonator coupled to a single InAs nanowire double quantum dot. The high frequency response of the circuit is used to probe the effects of the Pauli exclusion principle at interdot charge transitions. Even parity charge transitions show a striking magnetic field dependence that is due to a singlet-triplet transition, while odd parity transitions are relatively insensitive to magnetic field. The measured response agrees well with cavity input-output theory, allowing accurate measurements of the interdot tunnel coupling and the resonator-charge coupling rate g_c/2pi ~ 17 MHz.