In this study, the effect of various parameters of a single screw extruder on the rheology and mechanical properties of a polylactic acid (PLA) filament with a 1.75 mm diameter was investigated. The barrel temperature, nozzle and cooling bath temperature, screw speed, nozzle diameter, water bath length, and distance to the nozzle were the process variables. A Taguchi experimental design was implemented using an L8 orthogonal matrix with seven factors and two levels, and their influence on roundness and diameter were evaluated. Among the various processing parameters, the temperature of the cooling bath affected the roundness the most. The mechanical properties and surface roughness of the PLA filament were examined using a tensile test and nanofocus optical system, respectively. Moreover, to assess the filament’s reliability and investigate its behavior further, the filament was used to print 0° plates, and then dog-bone samples were cut from them to evaluate the mechanical properties of the printed specimens. Finally, the results indicate that improved-roundness filaments of 0.004 mm can lead to enhanced mechanical properties in 3D-printed samples with 3.54 MPa.