Using a data sample of \proton\proton collisions corresponding to an integrated luminosity of 3\invfb, collected with the LHCb detector at a centre-of-mass energies of 7 and 8 TeV, the $C\!P$-violating asymmetries in the decay and in the interference between mixing and decay in the $B^0\to\pi^+\pi^-$ and $B_s^0\to K^+K^-$ modes are measured. The results are $C_{\pi^+\pi^-} = -0.24 \pm 0.07 \pm 0.01$, $S_{\pi^+\pi^-} = -0.68 \pm 0.06 \pm 0.01$, $C_{K^+K^-} = 0.24 \pm 0.06 \pm 0.02$, $C_{K^+K^-} = 0.22 \pm 0.06 \pm 0.02$, and $C_{K^+K^-} = -0.75 \pm 0.07 \pm 0.11$, where the first uncertainties are statistical and the second systematic.