Cross subject functional studies of cerebral cortex require cortical registration that aligns functional brain regions. While cortical folding patterns are approximate indicators of the underlying cytoarchitecture, coregistration based on these features alone does not accurately align functional regions in cerebral cortex. This paper presents a method for cortical surface registration (rfDemons) based on resting fMRI (rfMRI) data that uses curvature-based anatomical registration as an initialization. In contrast to existing techniques that use connectivity-based features derived from rfMRI, the proposed method uses 'synchronized' resting rfMRI time series directly. The synchronization of rfMRI data is performed using the BrainSync transform which applies an orthogonal transform to the rfMRI time series to temporally align them across subjects. The rfDemons method was applied to rfMRI from the Human Connectome Project and evaluated using task fMRI data to explore the impact of cortical registration performed using resting fMRI data on functional alignment of the cerebral cortex.