Vacuum polarization integral involves the vector spectral functions which can be experimentally determined. As the dominant uncertainty source to the integral, the precision measurement of the %born cross section of $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ as a function of energy from $2\pi$ threshold to 3GeV is performed by taking the ratio of $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ cross section to $e^+e^-\rightarrow\mu^+\mu^-(\gamma)$ cross section which are both measured with {\babar\ }data using ISR method in one analysis. Besides that taking the ratio of the cross sections of the two processes can cancel several systematic uncertainties, the acceptance differences between data and MC are measured using the same data, and the corresponding corrections are applied on the efficiencies predicted by MC which can control the uncertainties. The achieved final uncertainty of the born cross section of $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ in $\rho$ mass region ($0.6\sim0.9$GeV) is 0.54\%. As a consequence of the new vacuum polarization calculation using the new precision result of the $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ cross section, the impact on the SM prediction of muon anomalous magnetic moment $g-2$ is presented, which is also compared with other data based predictions and direct measurement.