A new method for generating positrons has been proposed that uses betatron X-rays emitted by an electron beam in a high-K plasma wiggler. The plasma wiggler is an ion column produced by the head of the beam when the peak beam density exceeds the plasma density. The radial electric field of the beam blows out the plasma electrons transversely, creating an ion column. The focusing electric field of the ion column causes the beam electrons to execute betatron oscillations about the ion column axis. If the beam energy and the plasma density are high enough, these oscillations lead to synchrotron radiation in the 1-50 MeV range. A significant amount of electron energy can be lost to these radiated X-ray photons. These photons strike a thin (.5Xo), high-Z target and create e+/e- pairs. The experiment was performed at the Stanford Linear Accelerator Center (SLAC) where a 28.5 GeV electron beam with σr ≈ 10μm and σz ≈ 25μm was propagated through a neutral Lithium vapor (Li). The radial electric field of the dense beam was large enough to field ionize the Li vapor to form a plasma. The positron yield was measured as a function of plasma density, ion column length and electron beam pulse length. A computational model was written to match the experimental data with theory. The measured positron spectra are in excellent agreement with those expected from the calculated X-ray spectral yield from the plasma wiggler. After matching the model with the experimental results, it was used to design a more efficient positron source, giving positron yields of 0.44 e+/e-, a number that is close to the target goal of 1-2 e+/e- for future positron sources.