A coherently excited nuclear state in a rotating sample acquires a phase shift during its time evolution that is proportional to its angular momentum and the rotation angle. As a consequence, the radiative decay of the excited state proceeds into the rotated direction, and the time spectrum of the nuclear decay is mapped onto an angular scale. This effect has been observed in nuclear resonant scattering of synchrotron radiation from a 57Fe metal foil rotating at 18 kHz.