  Using a data set with an integrated luminosity of 2.93 fb$^{-1}$ taken at a
center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII
collider, we extract the $e^+e^-\rightarrow \pi^+\pi^-$ cross section and the
pion form factor $|F_\pi|^2$ in the energy range between 600 and 900 MeV. We
exploit the method of initial state radiation for this measurement, yielding a
systematic uncertainty of 0.9%. We calculate the contribution of the measured
cross section to the leading-order hadronic vacuum polarization contribution to
$(g-2)_\mu$.
