The problem of detecting a periodic signal buried in zero-mean Gaussian noise is present in various fields of engineering. It is well-known that the amplitude of the disturbed signal follows a Rice distribution which is characterized by two parameters. In this paper, an alternative Bayesian approach is proposed to tackle this two-parameter estimation problem. By incorporating prior knowledge into a mathematical framework, the drawbacks of the existing methods (i.e., the maximum likelihood approach and the method of moments) can be overcome. The performance of the proposed Bayesian estimatoris shown through simulations.