We present a measurement of the isolated direct photon cross section in p (p) over bar collisions at roots=1.8 TeV and \eta\<0.9 using data collected between 1994 and 1995 by the Collider Detector at Fermilab (CDF). The measurement is based on events where the photon converts into an electron-positron pair in the material of the inner detector, resulting in a two track event signature. To remove pi(0)-->gammagamma and eta-->gammagamma events from the data we use a new background subtraction technique which takes advantage of the tracking information available in a photon conversion event. We find that the shape of the cross section as a function of photon p(T) is poorly described by next-to-leading-order QCD predictions, but agrees with previous CDF measurements. RI Lancaster, Mark/C-1693-2008; Ruiz, Alberto/E-4473-2011; De Cecco, Sandro/B-1016-2012; Wolter, Marcin/A-7412-2012; St.Denis, Richard/C-8997-2012; Prokoshin, Fedor/E-2795-2012; Chiarelli, Giorgio/E-8953-2012; Azzi, Patrizia/H-5404-2012