Scale invariance is a characteristic of neural activity and how it emerges from neural interactions remains a fundamental question. Here, we studied the relation between scale-invariant brain dynamics and structural connectivity by analyzing human resting-state (rs-) fMRI signals, together with diffusion MRI (dMRI) connectivity and its approximation as an exponentially decaying function of the distance between brain regions. We analyzed the rs-fMRI dynamics using functional connectivity and a recently proposed phenomenological renormalization group (PRG) method that tracks the change of collective activity after successive coarse-graining at different scales. We found that brain dynamics display power-law correlations and power-law scaling as a function of PRG coarse-graining. Finally, by studying a whole-brain computational models, we showed that the observed scaling features emerge from critical dynamics and connections exponentially decaying with distance. In conclusion, our study validates the PRG method using large-scale brain activity and theoretical models and suggests that scaling of rs-fMRI activity relates to criticality and the geometry of the brain.