A quantum approach is presented to investigate tunneling time by supervising the instantaneous ionization rate. We find that the ionization rate peak appearance lags behind the maximum of electric field intensity for a linearly polarized pulse. This time delay interval can be taken to characterize the tunneling time. In addition, if an atom with anisotropic electronic distribution is exposed to a circular polarized pulse, the tunneling time can also be measured and defined as the time difference between the instant of the largest ionization rate and the moment when the electric field points in the maximum of the bound electron density.