  We demonstrate an accurate phase retrieval of XUV atomic ionization by
streaking the photoelectron in a circularly polarized IR laser field. The
streaking phase can then be converted to the atomic time delay containing the
Wigner and continuum-continuum components. Our demonstration is based on a
numerical solution of the time-dependent Schr\"odinger equation. We test this
technique using the hydrogen atom ionized by an isolated attosecond XUV pulse
across a wide range of photon energies. In parallel, we run a series of RABBITT
simulations and demonstrate equivalence of the phase and timing information
provided by the two methods. This validates the proposed technique and makes it
a useful tool that can be applied to a broad range of atomic and molecular
targets exposed to XUV radiation from novel free-electron laser sources.
