In this Letter, we present a new method for generation of circularly polarized attosecond pulses. According to our calculations, shape-controlled, carrier-envelope-phase stable pulses of several hundred nanojoule energy could be produced by exploitation of the coherent undulator radiation of an electron bunch. Our calculations are based on an existing particle accelerator system (FLASH II in DESY, Germany). We investigated the energy dependence of the attosecond pulses on the energy of electrons and the parameters of the radiator undulator, which generate the electromagnetic radiation.