As an important step toward an atomic parity violation experiment in one single trapped Ra+ ion, laser spectroscopy on short-lived Ra-212,213,214(+) ions was conducted. The isotope shift of the 6(2)D(3/2)-7(2)P(1/2) and 6(2)D(3/2)-7(2)P(3/2) transitions and the hyperfine structure constants of the 7(2)P(1/2) and 6(2)D(3/2) states in Ra-213(+) were measured, which provides a benchmark for the required atomic theory. A lower limit of 232(4) ms for 6(2)D(5/2) state lifetime was determined.</p