Atom interferometers (AIs) as gravitational-wave (GW) detector had been proposed a decade ago. Both ground and space-based projects will be in construction and preparation in a near future. In this paper, for the first time, we investigate the potential of the space-borne AIs on detecting GW standard sirens and hence the applications on cosmology. We consider AEDGE as our fiducial AI GW detector and estimate the number of bright sirens that would be obtained within a 5-years data-taking period. We then construct the mock catalogue of bright sirens and predict their ability on constraining such as the Hubble constant, dynamics of dark energy, and modified gravity theory. The preliminary results show that there should be of order $mathcal{O} (30)$ bright sirens detected within 5 years observation time by AEDGE. The bright sirens alone can measure $H_0$ with precision 2.1%, which is sufficient to arbitrate the Hubble tension. Combining current most precise electromagnetic experiments, the inclusion of AEDGE bright sirens can improve the measurement of equation of state of dark energy, though marginally. However, by modifying GW propagation on cosmological scales, the deviations from general relativity (modified gravity theory effects ) can be constrained at 5.7% precision level, which is two times better than by 10-years operation of LIGO, Virgo and KAGRA network.
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