We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite $Q^2$ with the derivative at $Q^2 = 0$. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to use the finite-$Q^2$ FF data for constraining the radius (up to $Q^2sim$ 0.5 GeV$^2$ and larger) and avoids the difficulties arising in methods relying on the $Q^2 rightarrow 0$ extrapolation. We obtain a radius of 0.844(7) fm, consistent with the high-precision muonic hydrogen results.
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