The electric field alignment of cylindrical microdomains in diblock copolymer thin films was studied using small-angle neutron scattering and transmission electron microscopy. The alignment process was followed with the block copolymer films in different initial states. Starting from a poorly ordered state, the cylindrical microdomain orientation was biased by the surface field that initially drove the cylindrical microdomains to be oriented parallel to the film surface. With further annealing, the cylinders were disrupted locally and formed ellipsoid-shaped microdomains that, with time, connected into cylindrical microdomains oriented in the field direction. Starting from an ordered state with cylinders parallel to the surface, the applied electric field enhanced fluctuations at the interfaces of the microdomains. The growth of the fluctuations continued until the cylindrical microdomains broke up into spherical microdomains, similar to that seen in the thermoreversible cylinder-to-sphere order-order transition. With time, the spherical microdomains deformed into ellipsoidal domains that reconnected into cylindrical microdomains oriented at similar to 45 degrees with respect to the applied field direction. Further annealing aligned the tilted cylinders along the applied field direction. This reorientation process was much slower than from the poorly ordered state. The details of the realignment process are supported by computer simulations based on dynamic self-consistent-field theory.