We discuss a method for direct and unambiguous measurement of ultrahigh laser intensities exceeding 10^20 W/cm2. The approach is based on the use of multiple sequential tunneling ionization of heavy atoms with sufficiently high ionization potentials. We show that, due to a highly nonlinear dependence of tunneling ionization rates on the electromagnetic field strength, an offset in the charge distribution of ions appears sufficiently sensitive to the peak value of intensity in the laser focus. A simple analytic theory is presented which helps in estimating the maximal charge state produced at a given intensity via the tunnel-ionization mechanism. The theory also allows for calculating qualitatively a distribution in charge states generated in different parts of the laser focus. We also study the sensitivity of the approach to two essential factors: the focal volume effect and the tunneling ionization model chosen to calculate ionization rates.