We present a density functional theory computational study of Li insertion into amorphous (α-)TiO₂ as well as the anatase, rutile, and bronze (B) phases. The computed defect formation energies in the crystalline phases are -1.38, -1.57, and -2.08 eV for anatase, rutile, and (B), respectively, vs. the reference state of bcc Li. Insertion sites in α-TiO₂ were identified with a clustering algorithm and further optimized by DFT. There is a distribution of insertion energies in α-TiO₂ ranging from -1.31 to -3.06 eV vs. Li metal. Amorphous TiO₂ is expected therefore to provide higher voltages at low Li concentrations than the crystalline phases.