A new and distinct Aloe aristata cultivar named ‘AMIAL1605’ which is characterized by a flattened globular plant shape, a short plant height, ovate foliage with an acute to broadly acute apex, and a short caudate tip dark green mature foliage with a moderately dense occurrence of prominent white papillae on both the adaxial and abaxial surfaces, as well as the stability of these characteristics from generation to generation.