© 2015 AIP Publishing LLC. Motivated by the interesting magnetic anisotropy found in the heavy fermion family CeTX2 (T = transition metal and X = pnictogen), here, we study the novel parent compound CeAu1-xBi2-y by combining magnetization, pressure dependent electrical resistivity, and heat-capacity measurements. The magnetic properties of our nearly stoichiometric single crystal sample of CeAu1-xBi2-y (x = 0.92 and y = 1.6) revealed an antiferromagnetic ordering at TN = 12 K with an easy axis along the c-direction. The field dependent magnetization data at low temperatures reveal the existence of a spin-flop transition when the field is applied along the c-axis (Hc ∼ 7.5 T and T = 5 K). The heat capacity and pressure dependent resistivity data suggest that CeAu0.92Bi1.6 exhibits a weak heavy fermion behavior with strongly localized Ce3+ 4f electrons. Furthermore, the systematic analysis using a mean field model including anisotropic nearest-neighbors interactions and the tetragonal crystalline electric field (CEF) Hamiltonian allows us to extract a CEF scheme and two different values for the anisotropic J RKKY exchange parameters between the Ce3+ ions in this compound. Thus, we discuss a scenario, considering both the anisotropic magnetic interactions and the tetragonal CEF effects, in the CeAu1-xBi2-y compounds, and we compare our results with the isostructural compound CeCuBi2.