We analyse 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 sourced by the different evolution of baryon and cold dark matter perturbations before decoupling. Our power spectrum model includes all $1$-loop redshift-space terms corresponding to $v_{rm bc}$ parameterised by the bias parameter $b_{v^2}$. We also include the linear terms proportional to the relative density, $delta_{rm bc}$, and relative velocity dispersion, $theta_{rm bc}$, which we parameterise with the bias parameters $b^{rm bc}_{delta}$ and $b^{rm bc}_{theta}$. 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 $b_{v^2} = 0.012 pm 0.015;(pm 0.031)$, $b^{rm bc}_{delta} = -1.0 pm 2.5;(pm 6.2)$ and $b^{rm bc}_{theta} = -114 pm 55;(pm 175)$ with $68%$ ($95%$) confidence levels. These constraints restrict the potential systematic shift in $D_A(z)$, $H(z)$ and $fsigma_8$, 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 $0.53sigma$, $0.5sigma$ and $0.22sigma$ for $D_A(z)$, $H(z)$ and $fsigma_8$, respectively.
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