We report a measurement of the single top quark production cross section in 2.2 fb{sup -1} of p{bar p} collision data collected by the Collider Detector at Fermilab at {radical}s = 1.96 TeV. Candidate events are classified as signal-like by three parallel analyses which use likelihood, matrix element, and neural network discriminants. These results are combined in order to improve the sensitivity. We observe a signal consistent with the standard model prediction, but inconsistent with the background only model by 3.7 standard deviations with a median expected sensitivity of 4.9 standard deviations. We measure a cross section of 2.2{sub -0.6}{sup +0.7}(stat+sys) pb, extract the CKM matrix element value |V{sub tb}| = 0.88{sub -0.12}{sup +0.13}(stat + sys) {+-} 0.07(theory), and set the limit |V{sub tb}| > 0.66 at the 95% C.L
