Optical trapping of selected species of radioactive atoms has great potential in precision measurements for testing fundamental physics such as the electric dipole moment, atomic parity nonconservation, and parity-violating $\ensuremath{\beta}$-decay correlation coefficients. We report on the trapping of
104 radioactive
82Rb atoms
(t1∕2=75s) with a trap lifetime of $\ensuremath{\sim}55\phantom{\rule{0.3em}{0ex}}\mathrm{s}$ in an optical dipole trap. Transfer efficiency from the magneto-optical trap is $\ensuremath{\sim}14%$. We further report evidence of spontaneous spin polarization of the atoms in optical dipole trap loading. These advancements are an important step toward a new generation of precision nuclear-spin--$\ensuremath{\beta}$-emission direction correlation measurements with polarized
82Rb atoms.