In this paper we calculate the binding energy of a donor impurity in the 1s-like state bound to X valleys of GaAs/AlAs type II quantum dots, using an anisotropic variational method, which allows us to take into account the anisotropy of the effective mass and quantum confinement. The binding energy is plotted against the radius of the cylinder and the uniform magnetic field applied along the cylinder axis. The binding energies have a monotone behavior with the cylinder radius for different magnetic fields and almost constant behavior with increasing magnetic field.