The dispersion of optical resonator structures can be used to increase the sensitivity of rotation sensing. Using coupled resonator waveguides can realize strong dispersion. In this paper, the transfer matrix method is used to analyze the phase sensitivity of rotation sensing in coupled resonator waveguides, and investigate the influences of resonator arrangement and waveguide parameters on the phase sensitivity. Results show that phase curves and phase sensitivity are dependent on resonator arrangement. The number of resonator and coupling coefficients can influence not only the number and bandwidths of peaks for phase sensitivity of rotation sensing but also the variation of phase sensitivity. However, loss can reduce the phase sensitivity. The results can be used to design the phase sensitivity of coupled resonator waveguides using the resonator arrangement and waveguide parameters, and are beneficial for applications of coupled resonator waveguides in rotation sensing.