We present a systematic Raman study of unconventionally-stacked double-layer graphene, and find that the spectrum strongly depends on the relative rotation angle between layers. Rotation-dependent trends in the position, width and intensity of graphene 2D and G peaks are experimentally established and accounted for theoretically. Our theoretical analysis reveals that changes in electronic band structure due to the interlayer interaction, such as rotational-angle dependent Van Hove

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... are responsible for the observed spectra features. Our combined experimental and theoretical study provides a deeper understanding of the electronic band structure of rotated double-layer graphene, and leads to a practical way to identify and analyze rotation angles of misoriented double-layer graphene.