Coherent extreme ultra-violet (XUV) and soft X-ray light with attosecond duration enable the time-resolved study of electron dynamics in a completely new regime. High order harmonic generation (HHG) from the highly nonlinear process of relativistically intense laser interactions with solid-density plasma offers a very new way to generate such a light source. In this paper, we study the HHG by a relativistically circularly polarized femtosecond laser interacting with solid-density plasma. The experiment is carried out by using a 200 TW Ti:sapphire laser system at the Laboratory for Laser Plasmas in Shanghai Jiao Tong University, China. The laser system can deliver laser pulses at 800 nm with a pulse duration (full width at half maximum, FWHM) of 25 fs and repetition rate of 10 Hz. The circularly polarized laser beam with an energy of 460 mJ is used in the experiment and focused by an F/4 off-axis parabolic mirror at an incidence angle of 40 with respect to the glass target. The focal spot diameter is 6 m (FWHM) with 25% energy enclosed, giving a calculated peak intensity of 1.61019 W/cm2. We detect high order harmonics by a flat-field spectrometer. The experimental results show that high order harmonic radiation can also be efficiently generated by a circularly polarized laser at a lager incidence angle, which provides a straightforward way to obtain a circularly polarized XUV light source. Different plasma density scale lengths are obtained by introducing a prepulse with different delays. We study the dependence of HHG efficiency on plasma density scale length by the circularly polarized laser, and find an optimal density scale length to exist. The influence of laser polarization and plasma density scale length on HHG are studied by two-dimensional (2D) PIC simulations. The good agreement is found between the 2D PIC simulations and experimental results. We plan to measure the polarization characteristics of high order harmonic produced by the interaction of circularly polarized lasers with solid target in the future. It is expected to obtain a compact coherent circularly polarized XUV light source, which can be used to study the ultra-fast dynamic process of magnetic materials.