The box-ball system (BBS) is a cellular automaton that exhibits the solitonic behavior. In recent years, with the rapid progress in the study of the hydrodynamics of integrable systems, there has been a growing interest in BBS with random initial distribution. In this talk, we consider the scaling limits for the tagged soliton in the BBS starting from certain stationary distribution. This is an ongoing work with Stefano Olla and Makiko Sasada.