In this work, the feasibility of microwave liquid crystal based dielectric waveguide phased shifters is investigated in a phased rod antenna array for the first time. For this, a 1×4 rod antenna array is designed including the phase shifters as well as a cascaded E-plane power divider network. As core elements, the phase shifter are designed as continuously tunable subwavelength fibers, partially filled with a newly specifically synthesized microwave liquid crystal, exhibiting a maximum FoM 145°/dB at 102.5GHz. As proof-of-concept, a simplified electric biasing network is developed, demonstrating its beam steering capability by changing the scanning angle between 0°, -25° and +15° with three different voltage distributions. The antenna array is well matched throughout the complete W-band with a input reflection below -10 dB. The measured antenna gain is between 11.5 to 9.1 dBi at 85 GHz accompanied with a side lobe level between -12 to -7 dB, depending on the steering configuration.