Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P− and T,P−violating interactions. The parameters of P− and T,P−odd terms of the spin-rotational Hamiltonian have been calculated for the 2 Σ electronic ground state of 223 RaF molecule. They include the Wa parameter, which is critical in experimental search for nuclear anapole moment and the parameters W d 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 223 Ra nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for 223 RaF and 223 Ra + have been computed as well, demonstrating the accuracy of the methods employed.