In this paper, we have studied a practical design of a broadband linear-to-circular polarizer based on a self-complementary metasurface composed of zigzag-shaped metal strips printed on a dielectric substrate. The term self-complementary indicates that the structure is identical to its complement, except for some translation smaller than the periodicity. This property together with the nonresonant response of the unit cells ensures broadband conversion from linear polarization to circular polarization. Although we have experimentally achieved a relative 3-dB-axial-ratio (AR) bandwidth (BW) of 53%, in principle, it could reach up to 70.5%. Moreover, the studied metasurface has a very small periodicity, which avoids any higher order grating lobes and provides angular stability of the phenomenon. In fact, the relative 3-dB-AR BW obtained in experiments stays always above 40% for incidence angles within ±30°. An excellent agreement was achieved among theory, simulations, and experiments.