Complex nanostructures such as branched semiconductor nanotetrapods are promising building blocks for next-generation nanoelectronics. Here we report on the electrical transport properties of individual CdS tetrapods in a field effect transistor (FET) configuration with a ferroelectric Ba(0.7)Sr(0.3)TiO(3) film as high-k, switchable gate dielectric. A cryogenic four-probe scanning tunneling microscopy (STM) is used to probe the electrical transport through individual nanotetrapods at different temperatures. A p-type field effect is observed at room temperature, owing to the enhanced gate capacitance coupling. And the reversible remnant polarization of the ferroelectric gate dielectric leads to a well-defined nonvolatile memory effect. The field effect is shown to originate from the channel tuning in the arm/core/arm junctions of nanotetrapods. At low temperature (8.5 K), the nanotetrapod devices exhibit a ferroelectric-modulated single-electron transistor (SET) behavior. The results illustrate how the characteristics of a ferroelectric such as switchable polarization and high dielectric constant can be exploited to control the functionality of individual three-dimensional nanoarchitectures.