The binding energy of a hydrogenic donor impurity in a zinc-blende GaN/AlGaN cylindrical quantum dot (QD) is calculated in the framework of effective-mass envelope-function theory using the plane wave basis. It is shown that the donor binding energy is highly dependent on the impurity position and QD size. The external electric field induces an asymmetrical distribution of the donor binding energy with respect to the center of the QD. The maximum of the donor binding energy is shifted from the center of the QD. The degenerating energy levels for symmetrical positions with respect to the center of QD are also split. The splitting increases with the increase in QD height while the splitting increases up to a maximum and then decreases with the increase in QD radius. In the presence of the external electric field, the donor binding energy is insensitive to dot height when the impurity is located at the left side of the QD with large dot height. In addition, Stark shift dependence on hydrogenic impurity position is calculated.