Using the data from the Proportional Counter Array (PCA) on board the Rossi X-Ray Timing Explorer satellite, we investigate the orbital modulation on the twin kilohertz quasi-periodic oscillations (kHz QPOs) previously detected by others in Circinus X-1. It is found that the twin kHz QPOs are exclusively scattered on the passage from the apastron (phase 0.5) to the next periastron (phase 1), which probably implies that a steady accretion disk is needed for producing the twin kHz QPOs. Our spectral analyses suggest that when the twin kHz QPOs are presented, the variation of the spectral parameters is relatively small, the spectra harden, and the spectral fluxes decrease. With increasing of the orbital phase, the frequencies of the twin kHz QPOs increase and the inner disk radius decreases. The iron line energy is positively correlated with the inner disk radius, which could be attributed to the gravitational red shift plus small Doppler red shift. From this correlation, the estimated low and upper limits of the neutron star are one time solar mass and three times solar mass, respectively.