An experimental investigation was performed to understand the quasi-static shear response of additively manufactured (AM) acrylonitrile butadiene styrene (ABS) via fusion deposition modeling (FDM). A modified flat hat-shaped (FHS) specimen configuration was used for shear testing. The main aim of this study was to investigate the effect of four different shear angles (0°, 5.44°, 13.39°, and 20.83°) and three printing orientations (vertical build, 0°/90°, and 45°/−45°) on the shear constitutive response and shear performance of FDM-printed ABS. Scanning electron microscopy images of the failure surface were used to explain the shear response of the material. The flow shear stress of the shear stress-strain response for vertically printed specimens demonstrated a monotonic increase up to a peak shear stress and then decrease at the end of the shear zone, while for 0°/90° specimens, an increasing trend until the peak value at the end of the shear zone was observed. With increasing shear angles, all specimens printed with three printing orientations exhibited increasing shear zone size and shear strength, and the 0°/90° specimens exhibited the highest shear strength for all four shear angles. However, the specimens of the 45°/−45° orientation demonstrated the highest increase in shear strength by about 60% and in the shear strain at the end of shear zone by about 175% as the shear angle was increased from 0° to 20.83°.