²²⁵Ra⁺ ions (nuclear spin I = 1/2) have transitions that are first-order insensitive to magnetic field noise, which is advantageous for optical clocks and quantum information science. We report on laser cooling and trap- ping of ²²⁵Ra⁺ ions and hyperfine splitting measurements of the ion’s 7s ²S_1/2, 7p ²P_1/2, and 6d ²D_3/2 states. We measured the ground-state hyperfine constant, A(S_1/2) = −27.684 511 052(5) GHz, and the quadratic Zeeman coefficient, C₂ = 142.3(1.0) Hz G^-2, of the ²S_1/2(F = 0, mF = 0) ↔ ²S_1/2(F = 1, mF = 0) transition. Our result addresses a discrepancy in the literature for the ground-state hyperfine splitting. We measured the hyperfine constants of the ²P_1/2 state, A(P_1/2 ) = −5.447(4) GHz, and the ²D_3/2 state, A(D_3/2) = −619.7(1.1) MHz. We also performed state preparation and measurement using the ground-state hyperfine levels and realized a fidelity of 0.9951(9).