  We report on the first Belle II measurement of the branching fraction
($\mathcal{B}$) and longitudinal polarization fraction ($f_L$) of $B^+\to
\rho^+\rho^0$ decays. We reconstruct $B^+\to \rho^+(\to \pi^+\pi^0(\to
\gamma\gamma))\rho^0(\to \pi^+\pi^-)$ decays in a sample of SuperKEKB
electron-positron collisions collected by the Belle II experiment in 2019 and
2020 at the $\Upsilon$(4S) resonance and corresponding to $62.8$ fb$^{-1}$ of
integrated luminosity. We fit the distributions of the difference between
expected and observed $B$ candidate energy, continuum-suppression variable,
dipion masses, and angular distributions of the resulting samples, to determine
a signal yield of $104\pm16$ events. The signal yields are corrected for
efficiencies determined from simulation and control data samples to obtain
$\mathcal{B}(B^+ \to \rho^+\rho^0) = [20.6 \pm 3.2(\rm stat) \pm 4.0(\rm
syst)]\times 10^{-6}$, and $f_L(B^+ \to \rho^+\rho^0) = 0.936
^{+0.049}_{-0.041}(\rm stat)\pm 0.021(\rm syst)$. This first Belle II $B^+ \to
\rho^+\rho^0$ angular analysis yields results compatible with previous
determinations, and indicates Belle II performance superior to early Belle
results.
