[en] The ρ meson self-energy in an isospin asymmetric pion gas at finite temperature and charged-pion chemical potential is evaluated. We utilize a conventional effective π-ρ Lagrangian and the functional integral representation of the partition function in the second order in the ρππ coupling constant. We analyze the gauge invariant rho meson polarization operator and its dependence on the invariant mass M and spatial momentum vertical stroke pvertical stroke of the ρ meson. The pole positions and the values of the imaginary parts of the self-energy for different polarization states have different functional dependences on M and vertical stroke pvertical stroke . The corresponding dielectron rate (calculated from the imaginary part of the polarization operators) shows a distinctive asymmetry when the momentum t=p₊-p_- is perpendicular or parallel to p, where p_± are the momenta of the electron pair. (orig.)