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. In these events, heavy flavor quarks from top quark decay are identified with a secondary vertex tagging algorithm. From 162  pb−1 of data collected by the Collider Detector at Fermilab, a total of 48 candidate events are selected, where 13.5±1.8 events are expected from background contributions. We measure a tt¯ production cross section of 5.6+1.2−1.1(stat.)+0.9−0.6(syst.)  pb.