We describe a new technique to measure the height of the X-ray limb with observations from occulted X-ray flare sources as observed by the RHESSI (the Reuven Ramaty High-Energy Spectroscopic Imager) satellite. This method has model dependencies different from those present in traditional observations at optical wavelengths, which depend upon detailed modeling involving radiative transfer in a medium with complicated geometry and flows. It thus provides an independent and more rigorous measurement of the true solar radius, meaning that of the mass distribution. RHESSIs measurement makes use of the flare X-ray sources spatial Fourier components (the visibilities), which are sensitive to the presence of the sharp edge at the lower boundary of the occulted source. We have found a suitable flare event for analysis, SOL2011-10-20T03:25 (M1.7), and report a first result from this novel technique here. Using a 4-minute integration over the 3-25 keV photon energy range, we find $R_{mathrm{X-ray}} = 960.11 pm 0.15 pm 0.29$ arcsec, at 1 AU, where the uncertainties include statistical uncertainties from the method and a systematic error. The standard VAL-C model predicts a value of 959.94 arcsec, about 1$sigma$ below our value.