We present a measurement of the tt production cross section using events with one charged lepton and jets from pp collisions at a center-of-mass energy of 1.96 TeV. A b-tagging algorithm based on the probability of displaced tracks coming from the event interaction vertex is applied to identify b quarks from top decay. Using 318  pb−1 of data collected with the CDF II detector, we measure the tt production cross section in events with at least one restrictive (tight) b-tagged jet and obtain 8.9+1.0−1.0(stat)+1.1−1.0(syst)  pb. The cross section value assumes a top quark mass of mt=178  GeV/c2 in the acceptance corrections. The dependence of the cross section on mt is presented in the paper. This result is consistent with other CDF measurements of the tt cross section using different samples and analysis techniques, and has similar systematic uncertainties. We have also performed consistency checks by using the b-tagging probability function to vary the signal-to-background ratio and also using events that have at least two b-tagged jets.