A technique is proposed to generate ultrashort coherent soft x-ray radiation in storage rings using angular-modulated electron beams. In the scheme a laser operating in the TEM01 mode is first used to modulate the angular distribution of the electron beam in an undulator. After passing through a special beam line with non-zero transfer matrix element $R_{54}$, the angular modulation is converted to density modulation which contains considerable higher harmonic contents of the laser. It is found that the harmonic number can be one or two orders of magnitude higher than the standard coherent harmonic generation method which relies on beam energy modulation. The technique has the potential of generating femtosecond coherent soft x-ray radiation directly from an infrared seed laser and may ope n new research opportunities for ultrafast sciences in storage rings. Show Partial Abstract