To measure microwatt-level laser power, this paper presents a method based on the atomic light shift effect. A 795 nm semiconductor laser is directed into a rubidium atomic clock with an output frequency of 10 MHz. To minimize the influence of laser frequency on power measurements, an experimental setup is implemented to precisely lock the laser frequency to the wavelength meter. After stabilizing the laser frequency, we analyze its correlation with the output frequency of the rubidium atomic clock. The experimental results indicate that, during free-running, the laser undergoes a frequency drift of -90 MHz over 2 hours, which is subsequently reduced to ±0.9 MHz over 40 hours through frequency locking. Moreover, by fixing the laser wavelength at 794.99 nm, we observe an increase in the atomic clock frequency shift with rising laser power. Specifically, a laser power of 2 μW corresponds to a frequency shift of 0.13 mHz at 10 MHz. This study achieves quantum measurement of weak laser power, significantly enhancing the accuracy of low-power laser measurements.