We present a measurement of the hyperfine splitting of the 6S(1/2) excited level of rubidium using two-photon absorption spectroscopy in a glass cell. The values we obtain for the magnetic dipole constant A are 239.18(03) MHz and 807.66(08) MHz for Rb-85 and Rb-87, respectively. The combination of the magnetic moments of the two isotopes and our measurements show a hyperfine anomaly in this atomic excited state. The observed hyperfine anomaly difference has a value of (87)delta(85)=-0.0036(2) due to the finite distribution of nuclear magnetization, the Bohr-Weisskopf effect.