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We consider compact Lie groups extensions of expanding maps of the circle,essentially restricting to U(1) and SU(2) extensions. The central object of thepaper is the associated Ruelle transfer (or pull-back) operator $\hat{F}$.Harmonic analysis yields a natural decomposition$\hat{F}=\oplus\hat{F}_{\alpha}$, where $\alpha$ indexes the irreduciblerepresentation spaces. Using Semiclassical techniques we extend a previousresult by Faure proving an asymptotic spectral gap for the family${\hat{F}_{\alpha}}$ when restricted to adapted spaces of distributions. Ourmain result is a fractal Weyl upper bound for the number of eigenvalues ofthese operators (the Ruelle resonances) out of some fixed disc centered on 0 inthe complex plane.

Fractal Weyl law for skew extensions of expanding maps