Numerical studies about the vortex-induced rotation (VIR) show that 6 regimes exist for square cylinder under VIR at small Reynolds numbers. Focusing on the small-amplitude oscillation regime, the paper proposes an analytical model of this regime by considering both the free streamline theory of inviscid flow around body and the boundary layer theory of viscous flow over a flat. The validity of this model is proved by comparing with numerical results using immersed boundary method. This paper also analyses the main driving force of small-amplitude oscillation and explains the reason of periodical oscillation.