We present a technique for 3D imaging of live cells in translational motion without need of axial scanning of objective lens. A set of transmitted electric field images of cells at successive points of transverse translation is taken with a focused beam illumination. Based on Hyugens' principle, angular plane waves are synthesized from E-field images of a focused beam. For a set of synthesized angular plane waves, we apply a filtered back-projection algorithm and obtain 3D maps of refractive index of live cells. This technique, which we refer to as synthetic aperture tomographic phase microscopy, can potentially be combined with flow cytometry or microfluidic devices, and will enable high throughput acquisition of quantitative refractive index data from large numbers of cells.