The scaling of magnetic fluctuations provides crucial information for the understanding of solar wind turbulence. However, the observed magnetic fluctuations contain not only turbulence but also magnetic structures, leading to the violation of time stationarity. This violation would conceal the true scaling and influence the determination of the sampling angle with respect to the local background magnetic field. Here, to investigate scaling anisotropy, we utilize a simple but effective criterion ϕ < 10° to ensure the time stationarity of the magnetic field, where ϕ is the angle between the two averaged magnetic fields after cutting the interval into two halves. We study the scaling anisotropy using higher-order statistics of structure functions under the condition of stationarity for near-Sun solar wind turbulence for the first time based on measurements obtained from the Parker Solar Probe at 0.17 au. We find that the scaling indices ξ of the magnetic field show a linear dependence on the order p close to ξ(p) = p/4. The multifractal scaling of the magnetic-trace structure functions becomes monoscaling close to ξ(p) = p/3 with the local magnetic field perpendicular to the sampling direction and close to ξ(p) = p/4 with the local magnetic field parallel to the sampling direction when measured with the stationary background magnetic field. The scaling of the velocity-trace structure functions has similar but less significant changes. The near-Sun solar wind turbulence displays different scaling anisotropies from the near-Earth solar wind turbulence, suggesting the evolution of the nonlinear interaction process during solar wind expansion.