Using a nonperturbative scattering theory, we study the photoelectron angular distributions (PADs) of Kr atoms irradiated by an infinite sequence of intense single-cycle pulses of circular polarization. We demonstrate the inversion asymmetry of PADs and the dependence of PADs on the carrier-envelope phase of the single-cycle pulses. The inversion asymmetry is caused by the interference between transition channels where the different channels are characterized by different combinations of absorbed-photon numbers in the ionization process. Our results provide a possible method to determine the value of carrier-envelope phase by the detected PADs.