The features of the electron energy spectrum in eccentric two-dimensional GaAs-AlGaAs quantum rings of circular shape are theoretically investigated taking into account the effect of externally applied magnetic and intense laser fields. Analytical expressions for the laser-dressed confining potential in this kind of quantum ring geometry are reported for the first time. Finite element method is used to solve the resulting single-particle effective mass two-dimensional partial differential equation. It is shown that the allowed level spectrum is greatly influence by the external probe as well as by the breaking of geometric symmetry related to the changes in eccentricity. In presence of an intense laser field, the conduction band confining profile suffers strong modifications along the structure, with an additional contribution to symmetry breaking. These modifications of electronic quantum states reflect in the intraband optical absorption. Accordingly, the features of the intraband transitions are discussed in detail, revealing the significant influence of the magnetic field strength and laser field intensity and polarization, together with eccentricity, in the allowing of ground-to-excited states transitions and their corresponding intensities.