Although Wi-Fi is an ideal technology for many ranging applications, the performance of current methods is limited by the system bandwidth, leading to low accuracy of $\sim 1$ m. For many applications, measuring differential range, viz., the change in the range between adjacent measurements, is sufficient. Correspondingly, this work proposes WiDRa - a Wi-Fi based Differential Ranging solution that provides differential range estimates by using the sum-carrier-phase information. The proposed method is not limited by system bandwidth and can track range changes even smaller than the carrier wavelength. The proposed method is first theoretically justified, while taking into consideration the various hardware impairments affecting Wi-Fi chips. In the process, methods to isolate the sum-carrier phase from the hardware impairments are proposed. Extensive simulation results show that WiDRa can achieve a differential range estimation root-mean-square-error (RMSE) of $\approx 1$ mm in channels with a Rician-factor $\geq 7$ (a $100 \times$ improvement to existing methods). The proposed methods are also validated on off-the-shelf Wi-Fi hardware to demonstrate feasibility, where they achieve an RMSE of $< 1$ mm in the differential range. Finally, limitations of current investigation and future directions of exploration are suggested, to further tap into the potential of WiDRa.