We present a measurement of the top-quark pair-production cross section in p (p) over bar collisions at root s = 1.96 TeV using a data sample corresponding to 1.7 fb(-1) of integrated luminosity collected with the Collider Detector at Fermilab. We reconstruct t (t) over bar events in the lepton + jets channel, consisting of e nu + jets and mu nu + jets final states. The dominant background is the production of W bosons in association with multiple jets. To suppress this background, we identify electrons from the semileptonic decay of heavy-flavor jets ("soft electron tags''). From a sample of 2196 candidate events, we obtain 120 tagged events with a background expectation of 51 +/- 3 events, corresponding to a cross section of sigma(t (t) over bar) = 7.8 +/- 2.4(stat) +/- 1.6(syst) +/- 0.5(lumi) pb. We assume a top-quark mass of 175 GeV/c(2). This is the first measurement of the t (t) over bar cross section with soft electron tags in run II of the Tevatron. RI De Cecco, Sandro/B-1016-2012; Robson, Aidan/G-1087-2011; St.Denis, Richard/C-8997-2012; Prokoshin, Fedor/E-2795-2012; Ruiz, Alberto/E-4473-2011