The present study introduces a Gauss-Seidel fluid-structure interaction (FSI) method including the flow solver, structural statics solver and a fast data transfer technique, for the research of structural deformation and flow field variation of rotor blades under the combined influence of steady aerodynamic and centrifugal forces. The FSI method is illustrated and validated by the static aeroelastic analysis of a transonic compressor rotor blade, NASA Rotor 37. An improved local interpolation with data reduction (LIWDR) algorithm is introduced for fast data transfer on the fluid-structure interface of blade. The results of FSI calculation of NASA Rotor 37 show that when comparing with the radial basis function (RBF) based interpolation algorithm, LIWDR meets the interpolation accuracy requirements, while the calculation cost can be greatly improved. The data transmission time is only about 1% of that of RBF. Moreover, iteration step of steady flow computation within one single FSI has little impact on the converged aerodynamic and structural results. The aerodynamic force-caused deformation accounts for nearly 50% of the total. The effects of blade deformation to the variations of aerodynamic performance are given, demonstrating that when static aeroelasticity is taken into account, the choke mass flow rate increases and the peak adiabatic efficiency slightly decreases. The impact mechanisms on performance variations are presented in detail.