Context : Galactic foreground emission fluctuations are a limiting factor for precise cosmic microwave background ( CMB ) anisotropy measurements . Aims : We intend to improve current estimates of the influence of Galactic synchrotron emission on the analysis of CMB anisotropies . Methods : We perform an angular power spectrum analysis ( APS ) of all-sky total intensity maps at 408 MHz and 1420 MHz , which are dominated by synchrotron emission out of the Galactic plane . We subtract the brighter sources from the maps , which turns out to be essential for the results obtained . We study the APS as a function of Galactic latitude by considering various cuts and as a function of sky position by dividing the sky into patches of \sim 15 ^ { \circ } \times 15 ^ { \circ } in size . Results : The APS of the Galactic radio diffuse synchrotron emission is best fitted by a power law , C _ { \ell } \sim k \ell ^ { \alpha } , with \alpha \in [ -3.0 , -2.6 ] , where the lower values of \alpha typically correspond to the higher latitudes . Nevertheless , the analysis of the patches reveals that strong local variations exist . A good correlation is found between the APS normalized amplitude , k _ { 100 } = k \times 100 ^ { \alpha } , at 408 MHz and 1420 MHz . The mean APS for \ell \in [ 20 , 40 ] is used to determine the mean spectral index between 408 MHz and 1420 MHz , \beta _ { ( 0.408 - 1.4 ) { GHz } } \in [ -3.2 , -2.9 ] ( C _ { \ell } ( \nu ) \propto \nu ^ { -2 \beta } ) , which is then adopted to extrapolate the synchrotron APS results to the microwave range . Conclusions : We use the 408 MHz and 1420 MHz APS results to predict the Galactic synchrotron emission fluctuations at frequencies above 20 GHz . A simple extrapolation to 23 GHz of the synchrotron emission APS found at these radio frequencies does not explain all the power in the WMAP synchrotron component even at middle/high Galactic latitudes . This suggests a significant microwave contribution ( of about 50 \% of the signal ) by other components such as free-free or spinning dust emission . The comparison between the extrapolated synchrotron APS and the CMB APS shows that a mask excluding the regions with |b _ { gal } | \lesssim 5 ^ { \circ } would reduce the foreground fluctuations to about half of the cosmological ones at 70 GHz even at the lowest multipoles . The main implications of our analysis for the cosmological exploitation of microwave temperature anisotropy maps are discussed .