We analyze the power spectrum of the Baryon Oscillation Spectroscopic Survey (BOSS), Data Release 12 (DR12) 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 caused by a relative density δbc between baryons and cold dark matter at decoupling, which sources a relative velocity vbc between the two components. Our power spectrum model includes all 1-loop redshift-space terms corresponding to vbc parameterized by the bias parameter bv2. We also include the linear terms proportional to δbc and θbc which we parameterize 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 bv2=0.012±0.015(±0.031), bbcδ=−1.0±2.5(±6.2) and bbcθ=−114±55(±175) with 68% (95%) confidence levels. These constraints restrict the potential systematic shift in DA(z), H(z) and fσ8, due to the relative velocity, to 1%, 0.8% and 2%, 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.