We report the first measurements of the moments -mean ($M$), variance ($\sigma^{2}$), skewness ($S$) and kurtosis ($\kappa$) -of the net-charge multiplicity distributions at mid-rapidity in Au+Au collisions at seven energies, ranging from $\sqrt {{s_{\rm NN}}}$=7.7 to 200 GeV, as a part of the Beam Energy Scan program at RHIC. The moments are related to the thermodynamic susceptibilities of net-charge, which are expected to diverge at the QCD critical point. We compare the products of the moments, $\sigma^{2}/M$, $S\sigma$ and $\kappa\sigma^{2}$ with the expectations from Poisson and negative binomial distributions (NBD). The $S\sigma$ values deviate from Poisson and are close to NBD baseline, while the $\kappa\sigma^{2}$ values tend to lie between the two. Within the present uncertainties, our data do not show clear evidence of non-monotonic behavior as a function of collision energy.