  The branching fraction and direct $C\!P$ asymmetry of the decay
$B^{+}\rightarrow J/\psi \rho^{+}$ are measured using proton-proton collision
data collected with the LHCb detector at centre-of-mass energies of 7 and 8
TeV, corresponding to a total integrated luminosity of 3$\mbox{fb}^{-1}$. The
following results are obtained: \begin{align} \mathcal{B}(B^{+}\rightarrow
J/\psi \rho^{+}) &= (3.81 ^{+0.25}_{-0.24} \pm 0.35) \times 10^{-5}, \nonumber
\\ \mathcal{A}^{C\!P} (B^{+}\rightarrow J/\psi \rho^{+}) &=
-0.045^{+0.056}_{-0.057} \pm 0.008, \nonumber \end{align} where the first
uncertainties are statistical and the second systematic. Both measurements are
the most precise to date.
