A laboratory device, Differential Acoustic Resonance Spectroscopy (DARS), has been developed to investigate the acoustic properties of rock materials below 1 KHz. The device is based on analyzing shifts of resonance frequency of a cavity perturbed by the presence of a small sample. Numerical and experimental studies have previously shown that this technique can be used to estimate the compressibility of samples. In this study, we adopt a nonlinear least-squares whole-curve-fitting inversion approach, which for the first time allows estimation of both the compressibility and density of rock samples. In comparison to previous estimation techniques, this inversion method provides more reliable estimation of rock acoustic properties. This research proves that the DARS laboratory device, in conjunction with the calibration technique proposed herein, is a useful tool to estimate the properties of small rock samples. In addition, the simultaneous estimation of compressibility and density can potentially provide information on porosity and, by extension, a link between porosity and acoustic modulus at low frequency.