This study presents a novel tomographic imaging technique for living biomedical samples using an optically driven full-angle rotation scheme based on digital holographic microscopy, in which the three-dimensional refractive index distribution inside the sample can be measured and analyzed. To accomplish the full-angle sample rotation, two optical traps are driven by highly focused spots on the top and bottom of the sample. The rim image of the sample outside the focal depth at the different rotation angles and propagation distances can be corrected and compensated, respectively, via numerical focusing; therefore, tomographic imaging of the sample can be conducted. The proposed approach shows that an entire symmetric spectrum can be acquired for tomographic reconstruction without the missing apple core problem as in traditional sample-rotation schemes. The three-dimensional refractive index of living yeast in a fluid medium is measured and verified.