Asymmetry of the photodetachment of F by few-cycle circularly polarized infrared laser fields is studied by using a nonperturbative quantum scattering theory.The asymmetry of photoelectrons emitted to a pair of two opposite directions for low laser peak intensities is found and the dependence of the asymmetry on the laser peak intensity is investigated.It is found that the asymmetry degree varies with the carrier-envelope (CE) phase as a sine-like patte.The asymmetry degree, the value of the maximal asymmetry degree and the value of the CE phase corresponding to the maximal asymmetry degree vary with the laser peak intensity dramatically.At higher laser intensities, the asymmetry is still distinctive for relatively-long few-cycle pulses.It provides a possible means to measure the CE phase of laser pulses at lower intensities.