AbstractA small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe₂As₂, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature T_s. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature T_N ( < T_s) and create in-plane resistivity anisotropy above T_s. Here we use neutron polarization analysis to show that such a strain on BaFe₂As₂ also induces a static or quasi-static out-of-plane (c-axis) AF order and its associated critical spin fluctuations near T_N/T_s. Therefore, uniaxial pressure necessary to detwin single crystals of BaFe₂As₂ actually rotates the easy axis of the collinear AF order near T_N/T_s, and such effects due to spin-orbit coupling must be taken into account to unveil the intrinsic electronic/magnetic properties of the system.