We have developed a method to estimate surface gravity (log g) from light curves by measuring the granulation background, similar to the 'flicker' method by Bastien et al. (2016ApJ...818...43B, Cat. J/ApJ/818/43) but working in the Fourier power spectrum. We calibrated the method using Kepler stars for which asteroseismology has been possible with short-cadence data, demonstrating a precision in log g of about 0.05dex. We also derived a correction for white noise as a function of Kepler magnitude by measuring white noise directly from observations. We then applied the method to the same sample of long-cadence stars as Bastien et al. We found that about half the stars are too faint for the granulation background to be reliably detected above the white noise. We provide a catalogue of log g values for about 15000 stars having uncertainties better than 0.5dex. We used Gaia DR2 parallaxes to validate that granulation is a powerful method to measure log g from light curves. Our method can also be applied to the large number of light curves collected by K2 and TESS.