In this paper we suggest a convenient quantum statistical approach to calculate the critical rotation frequency for vortex nucleation in a rotating condensate boson atoms. We extende the quantum mecanices approach for achieving the critical rotation rate to enclode the effect of finite temperature. Dependence of the critical rotation on the interatomic interaction, atoms number and temperature is considered. A simple semiclassical approach is suggested. The calculated results showed that the critical rotation rate α depending crucially on the above mensioned parameters, its change very rapidly at very low temperature. Which means that the vortical configuration is achieved for an accurate
rotation rate value α, depends on temperature, interatomic interaction and number of condensate atoms. The obtained results provide useful qualitative theoretical results for future Bose Einstein condensation experiments in rotating traps. Motivated by our work, it will be interesting to study the critical rotation for vortex nucleation of rotating condensate boson atoms in optical lattice.