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 $$\,\text{ fb }^{-1}$$ . The following results are obtained: $$\begin{aligned} \mathcal {B}({{B} ^+} \!\rightarrow {{J /\psi }} {{\rho } ^+} )&= (3.81^{+0.25}_{-0.24} \pm 0.35) \times 10^{-5},\\ \mathcal {A}^{{C\!P}} ({{B} ^+} \!\rightarrow {{J /\psi }} {{\rho } ^+} )&= -0.045^{+0.056}_{-0.057} \pm 0.008, \end{aligned}$$ where the first uncertainties are statistical and the second systematic. Both measurements are the most precise to date.