The anisotropic creep response in both the XY and XZ planes of Ti–6Al–4V ELI manufactured by powder bed fusion (PBF) was examined under nanoindentation creep loading at room temperature, ranging from nm to μm scales. The stress exponent values of 4.06–4.30, rationalised through threshold stress, indicate that the creep behaviour is primarily dominated by dislocation gliding. Creep displacement results show that the anisotropic creep behaviour in the XY and XZ planes of the as-built, and heat treatment enhances the creep resistance of the XZ plane, while there is no significant difference in creep displacement between the as-built and heat-treated XY planes. Due to the higher dislocation density and compressive residual stress in the XY plane compared to the XZ plane, the creep resistance is higher in the XY plane for the as-built. It is highlighted that compressive residual stress is more relieved in the XY plane than in the XZ plane through heat treatment. The heat treatment results in improved creep resistance due to the formation of the Widmanstätten structure and β precipitates, which can impede dislocation movement under creep loading. The combination of residual stress and microstructural effects leads to anisotropic creep behaviour, suggesting that the anisotropy is inherited from the additive manufacturing process at micron scales.