  We report a measurement of the radium ion's $7p\,\, ^2\!P_{3/2}$ state
branching fractions and improved theoretical calculations. With a single
laser-cooled $^{226}\mathrm{Ra}^+$ ion we measure the $P_{3/2}$ branching
fractions to the $7s\,\,^2\!S_{1/2}$ ground state 0.87678(20), the
$6d\,\,^2\!D_{5/2}$ state 0.10759(10), and the $6d$ ${}^{2}D_{3/2}$ state
0.01563(21).
