  The inclusive $D_s^{\pm}$ production asymmetry is measured in $pp$ collisions
collected by the LHCb experiment at centre-of-mass energies of $\sqrt{s} =7$
and 8 TeV. Promptly produced $D_s^{\pm}$ mesons are used, which decay as
$D_s^{\pm}\to\phi\pi^{\pm}$, with $\phi\to K^+K^-$. The measurement is
performed in bins of transverse momentum, $p_{\rm T}$, and rapidity, $y$,
covering the range $2.5<p_{\rm T}<25.0$ GeV$/c$ and $2.0<y<4.5$. No kinematic
dependence is observed. Evidence of nonzero $D_s^{\pm}$ production asymmetry is
found with a significance of 3.3 standard deviations.
