This paper investigates the RF electrophoretic response of ellipsoidal gold nanoparticles (AuNPs). Since the existing works generally consider the electrophoretic heating of spherical AuNPs, this work provides an important step towards understanding the behavior of ellipsoidal AuNPs. We first develop an analytical framework for modeling of electrophoretic response of ellipsoidal AuNPs. Thereafter, due to the lack of experimental studies of non-spherical electrophoretic RF heating of AuNPs, we validate our theory by comparison to the existing experimental results of spherical AuNPs as a special case, and estimate a few additional parameters not considered before. Then, parameter studies are performed on surface charge, friction constant, frequency, and ionic background, with respect to AuNP size and shape. Finally, we present new results for the electromagnetic absorption and heat rates of ellipsoidal AuNPs in human tissue. Our results from the tissue testing indicate a strong difference between aqueous media and realistic human tissues due to the major difference in the host medium viscosity. We demonstrate the electrophoresis' strong dependency on the host medium's viscosity, where we note that cancer tissue viscosity is more than a thousand times higher than that of water. We thereby confirm negative results for RF AuNP heating, indicated by our own previous study and two other previous studies. Our results provide important insights into the feasibility of RF AuNP heating in a medical context.