  A measurement of the $C\P$ asymmetry in $B^+ \rightarrow K^+ \mu^+ \mu^-$
decays is presented using $pp$ collision data, corresponding to an integrated
luminosity of 1.0${\,fb}^{-1}$, recorded by the LHCb experiment during 2011 at
a centre-of-mass energy of 7 TeV. The measurement is performed in seven bins of
$\mu^+ \mu^-$ invariant mass squared in the range
${0.05<q^{2}<22.00{\mathrm{GeV^2/}c^4}}$, excluding the ${J/\psi}$ and
$\psi{(2S)}$ resonance regions. Production and detection asymmetries are
corrected for using the $B^+ \rightarrow J/\psi K^+$ decay as a control mode.
Averaged over all the bins, the $C\P$ asymmetry is found to be ${{\cal A}_{C\P}
= 0.000\pm 0.033{(stat.)} \pm0.005 {(syst.)} \pm 0.007{}(J/\psi K^+)}$, where
the third uncertainty is due to the $C\P$ asymmetry of the control mode. This
is consistent with the Standard Model prediction.
