A new method to measure the carrier-envelope phase (CEP) of a strong few-cycle laser pulse is introduced. The new concept relies on above threshold ionization (ATI) in circularly polarized laser fields and allows for CEP tagging every single laser pulse generated in few-cycle laser systems at multi-kHz repetition rates. The implementation of the new method is described and discussed quantitatively. It is shown that the introduced circular-polarization phase-meter may offer a series of advantages over existing CEP-tagging schemes based on ATI in linearly polarized laser fields.