Quasi-Thermal Noise (QTN) spectroscopy is a reliable diagnostic routinely used for measuring electron density and temperature in space plasmas. The observed spectrum depends on both antenna geometry and plasma kinetic properties. Parker Solar Probe (PSP), launched in 2018, is equipped with an antenna system consisting of two linear dipoles with a significant gap between the antenna arms. Such a configuration, not utilized on previous missions, cannot be completely described by current models of the antenna response function. In this work, we calculate the current distribution and the corresponding response function for the PSP antenna geometry, and use these results to generate synthetic QTN spectra. Applying this model to the Encounter 7 observations from PSP provides accurate estimations of electron density and temperature, which are in very good agreement with particle analyzer measurements.