Highly attenuated laser pulses based on Gaussian beams are used as single-photon sources. It is assumed that this laser beam has an initial Gaussian temporal pulse shape and a TEM01 mode Laguerre-Gaussian spatial profile. Based on the Rytov approximation and the modified von Karman spectrum model of refractive-index fluctuations, the influence of atmospheric turbulence on a single-photon acquisition probability in satellite-ground quantum communications was studied. Theoretical models of the single-photon acquisition probability in an uplink channel and a downlink channel were established. The single-photon acquisition probability was analyzed for laser links between a ground station and a satellite in a low earth orbit. The results show that, the single-photon acquisition probability in the uplink channel depends strongly on the refractive-index structure parameter at the ground C2n(0) and decreases as C2n(0) increasing. However, in the downlink channel the single-photon acquisition probability does not depend on C2n(0), that is, atmospheric turbulence has little influence on it.