Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. In the variational treatment, the Coulomb potentials are emulated by harmonic repulsive forces between all monomers; the force constants are used as variational parameters. The accuracy of the variational approach is tested against Monte Carlo data. Excellent agreement is obtained for the end-to-end separation and the apparent dissociation constant for the unscreened Coulomb chain. The short-range screened Coulomb potential is more difficult to handle variationally, and its structural features are less well described, although the thermodynamic properties are predicted with the same accuracy as for the unscreened chain. The number of variational parameters is on the order of N-2, where N is the number of monomers, and the computational effort scales like N-3. In addition, a simplified variational procedure with only two parameters is pursued, based on a rigid-rod approximation of the polymer. It gives surprisingly good accuracy for certain physical properties.