Recently, BICEP2 measurements of the cosmic microwave background (CMB) B-mode polarization has indicated the presence of primordial gravitational waves at degree angular scales, inferring the tensor-to-scalar ratio of r=0.2 and a running scalar spectral index. In this {\em Letter}, we show that the existence of the fluctuations of cosmological birefringence can give rise to CMB B-mode polarization that fits BICEP2 data with r<0.11 and no running of the scalar spectral index. Thus, it might be too hasty to conclude that many inflation models with small r are ruled out based on BICEP2 result.
