We study and demonstrate the frequency conversion of UV radiation, resonant with 369.5 nm transition in Yb+ ions to the C-band wavelength 1580.3 nm and vice-versa using a reverse proton-exchanged waveguide in periodically poled lithium niobate. Our integrated device can interface trapped Yb+ ions with a telecom infrastructure for the realization of an Yb+ based quantum repeater protocol and to efficiently distribute entanglement over long distances. We analyse the single photon frequency conversion efficiency from the 369.525 nm to the telecom wavelength and its dependence on pump power, device length and temperature. The single-photon noise generated by the spontaneous Raman scattering of the pump is also measured. From this analysis we estimate a single photon conversion efficiency of ~9% is achievable with our technology with almost complete suppression of the Raman noise.