Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P- and T-and-P–violating interactions. The parameters of P- and T,P-odd terms of the spin-rotational Hamiltonian have been calculated for the 2Σ electronic ground state of the RaF223 molecule. They include the Wa parameter, which is critical in the experimental search for nuclear anapole moment, and the parameters Wd and WSP required to obtain restrictions on the electric dipole moment of the electron and T,P-odd scalar-pseudoscalar interactions, respectively. The parameter X corresponding to the “volume effect” in the T,P-odd interaction of the Ra223 nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for RaF223 and 223Ra+ have been computed as well, demonstrating the accuracy of the methods employed.