A variational calculation within the effective-mass approximation of the ground and lowest excited states of a donor impurity in a cylindrical GaAs-(Ga,Al)As quantum-well wire is presented. The corresponding impurity binding energies are calculated for various values of the GaAs-(Ga,Al)As quantum-wire radius and donor positions within the wire. The line strengths of transitions from the donor ground state to excited states of 2s-like and 2p(z)-like symmetries are calculated as the donor position varies along the radial direction in the wire, for polarizations of the incident radiation perpendicular and parallel to the wire axis, respectively. Although the 1s-->2s donor transition is forbidden in bulk materials, this transition is allowed for incident radiation polarized along the y radial direction of the wire with a quite considerable oscillator strength-comparable to the strength of the 1s-->2p(z) transition-for impurities away from the wire axis.49151045010455