The vacancy can be produced through impact ionization of target atom by energetic particles. It is of significant importance to study the vacancy state by the measurement of angular distribution of typical X-rays. At present, accurate ionization cross-section data of the atomic inner shell are urgently required in many areas. However, the precise measurement of ionization cross-section of the atomic inner shell is largely dependent on the fact that whether the characteristic radiation (e.g., X-ray) is isotropic.In this experiment, the characteristic L_ι, L_α, L_β and L_γ1 X-rays for Au target are measured by a silicon drift detector in an emission angle range from 130° to 170° in steps of 10°. A mini-X ray source is utilized to produce bremsstrahlung with the center energy of 13.1 keV. Considering detection efficiency of the detector and the absorption of the target, relative intensity ratios, I(L_α)/I(L_γ1) and I(L_ι)/I(L_γ1), are obtained at different detection angles based on the experimental energy spectrum results. Moreover, the angular dependence of X-ray intensity ratio is investigated and it is found that the X-rays L_ι and L_α exhibit anisotropic emission. According to the X-ray intensity ratio I(L_ι)/I(L_γ1) and the P₂(cosθ), and using the least square method, the anisotropic parameter β of characteristic X-ray L_ι is derived to be 0.25. Due to the relation β = ακA₂₀, the value of the alignment degree A₂₀ for L₃ sub-shell is determined to be 0.577 ± 0.08. Alignment degree A₂₀ for L₃ sub-shell is dependent on its intrinsic physical properties, while the anisotropy parameter β of typical X-rays can be affected by Coster-Kronig transition process. The behavior of the alignment for inner-shell vacancy states calls for more research results both in theory and in experiment. Therefore, it is quite relevant and meaningful to perform more experiments to further study the angular distribution of vacancy states by electrons, photons and ions impacting a target.