For the applications of the frequency comb in microresonators, it is essential to obtain a fully frequency-stabilized microcomb laser source. Here, we demonstrate an atom-referenced stabilized soliton microcomb generation system based on the integrated microring resonator. The pump light around \(1560.48\,\mathrm{nm}\) locked to an ultra-low-expansion (ULE) cavity, is frequency-doubled and referenced to the atomic transition of \(^{87}\mathrm{Rb}\). The repetition rate of the soliton microcomb is injection-locked to an atomic-clock-stabilized radio frequency (RF) source, leading to mHz stabilization at \(1\) seconds. As a result, all comb lines have been frequency-stabilized based on the atomic reference and could be determined with very high precision reaching \(\sim18\,\mathrm{Hz}\) at 1 second, corresponding to the frequency stability of \(9.5\times10^{-14}\). Our approach provides an integrated and fully stabilized microcomb experiment scheme with no requirement of \(f-2f\) technique, which could be easily implemented and generalized to various photonic platforms, thus paving the way towards the portable and ultraprecise optical sources for high precision spectroscopy.