We analyse the power spectrum of the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 to constrain the relative velocity effect, which represents a potential systematic for measurements of the baryon acoustic oscillation (BAO) scale. The relative velocity effect is sourced by the different evolution of baryon and cold dark matter perturbations before decoupling. Our power spectrum model includes all one-loop redshift-space terms corresponding to vbc parametrized by the bias parameter b2v. We also include the linear terms proportional to the relative density, δbc, and relative velocity dispersion, θbc, which we parametrize with the bias parameters bbcδ and bbcθ. Our data does not support a detection of the relative velocity effect in any of these parameters. Combining the low- and high-redshift bins of BOSS, we find limits of b2v=0.012±0.015(±0.031), bbcδ=−1.0±2.5(±6.2) and bbcθ=−114±55(±175) with 68 per cent (95 per cent) confidence levels. These constraints restrict the potential systematic shift in DA(z), H(z) and fσ8, due to the relative velocity, to 1 per cent, 0.8 per cent and 2 per cent, respectively. Given the current uncertainties on the BAO measurements of BOSS, these shifts correspond to 0.53σ, 0.5σ and 0.22σ for DA(z), H(z) and fσ8, respectively.