We present an algorithm for reconstruction of isolated attosecond pulses, which exploits
the phase dependent energy modulation of a photoelectron ionized in the presence of a strong circularly polarized laser field from the angle-resolved photoelectron momentum distributions. Complete reconstruction of the temporal and spectral profile of an attosecond burst are allowed. We show that this type of reconstruction algorithm is robust against counting noise and suitable for single-shot experiments. This algorithm holds potential for a variety of applications for attosecond pulse sources.