We present a measurement of the t-tbar production cross section using events with one charged lepton and jets from p-pbar 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. Backgrounds are computed from data and Monte Carlo simulation. Using 318 inverse pb of data collected with the CDF II detector, we measure the t-tbar 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.) inverse pb. The cross section value assumes a top quark mass of 178 GeV in the acceptance corrections. The dependence of the cross section on the top quark mass is presented in the paper. This result is consistent with other CDF measurements of the t-tbar 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.