Frequency-resolved laser-induced gamma-ray anisotropy has been achieved and used to measure the D1 hyperfine structure of the 1-s isomer Rbm85. The magnetic dipole moment obtained is (6.046±0.010)N and the isomer shift relative to Rb85 is 52±9 MHz. The experiment was performed with a sealed cell containing radioactive Kr85 (3 mCi) and natural Rb(10 mTorr). This method is simple and convenient and promises to be of wide usefulness. © 1984 The American Physical Society.