This manuscript presents a wavelength-division multiplexing (WDM)-based photonic beamformer for an RF phased array antenna transmitter, capable of simultaneously generating multiple beams using the same optical spectrum. In the proposed architecture, for each RF beam, a WDM signal comprising the modulated RF sidebands undergoes complex-valued filtering, while another WDM signal with the same channels, but carrying only optical carriers, goes through an optical frequency-shifting stage. The proposed architecture allows the same WDM channels to be reused for multiple RF beams. The detection of the frequency-shifted optical carrier and the filtered RF sideband of each WDM channel at the photodetector produces a frequency-converted, correctly weighted signal to be fed to each antenna element. The features described herein are analytically derived, numerically simulated, and experimentally demonstrated. Results showcase two independent beams being transmitted in different directions.