We present variational calculations of donor binding energy in rectangular wurtzite aluminium gallium nitride / gallium nitride quantum wires. We explicitly take into account the effect of spontaneous and piezoelectric polarization on the energy levels of donors in quantum wires. Wurtzite structure nitride semiconductors have spontaneous polarization even in the absence of externally applied electric fields. They also have large piezoelectric polarization when grown as pseudomorphic layers. The magnitude of both polarization components is of the order of 1013 electrons per cm2, and has a non-trivial effect on the potential profile seen by electrons. Due to the large built-in electric fields resulting from the polarization discontinuities at heterojunctions, the binding energies of donors is a strong function of the position inside the quantum wire. The potential profile in the 0001 direction can vary by as much as 1.5eV due to polarization effects for vertical dimensions of the quantum wire up to 20 angstroms. The probability density of electrons tends to concentrate near the minimum of the conduction band profile in the 0001 direction. Donors located close to this minimum tend to have a larger concentration of electron density compared to those located closer to the maximum. As a consequence, the binding energy of the former are higher compared to the latter. We use Lorentzian variational wavefunctions to calculate the binding energy as a function of donor position. The confinement potential enhances the binding by a factor of about 3 compared to donors in bulk nitride semiconductors, from about 30 meV to about 90 meV. The variation of binding energy with position is calculated to be more than 50% for typical compositions of the quantum wire regions. Our calculations will be useful for understanding device applications involving n-type doped nitride semiconductor quantum wires.