A measurement of the $C\!P$ asymmetry in $B^0 \rightarrow K^{*0} \mu^+ \mu^-$ decays is presented, based on 1.0 fb$^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011. The measurement is performed in six bins of invariant mass squared of the $\mu^+\mu^-$ pair, excluding the $\mathrm{J}\mskip -3mu/\mskip -2mu\psi\mskip 2mu$ and $\psi(2S)$ resonance regions. Production and detection asymmetries are removed using the $B^0 \rightarrow \mathrm{J}\mskip -3mu/\mskip -2mu\psi\mskip 2mu K^{*0}$ decay as a control mode. The integrated $C\!P$ asymmetry is found to be $-0.072 \pm 0.040 \mbox{ (stat.)} \pm 0.005 \mbox{ (syst.)}$, consistent with the Standard Model.