The frequency stability of long-distance two-way fiber-optic radio frequency (RF) transfer is directly affected by the optical signal-to-noise ratio (OSNR) of optical amplifiers. In this paper, we have proposed a stimulated Brillouin scattering (SBS)-based optical amplification scheme with high OSNR for two-way fiber-optic RF frequency transfer over single mode fibers (SMF). At the remote and local site, the modulated carrier transferred from the opposite was amplified and then frequency upshifted by Brillouin frequency shift (BFS) for pump generation. This approach can avoid the use of additional pump lasers and phase-locked loops for wavelength stabilization of the pump. The pump was injected into the fiber link and counter-propagated with the signal to amplify the modulated carrier. A 2.2 GHz RF signal transfer with the proposed SBS-based optical amplification schemes was demonstrated over a 100 km fiber link. The experimental results illustrated that the OSNR was increased by 35 dB and 32 dB at the local site and the remote site, respectively, compared to the results obtained with erbium-doped fiber amplifiers (EDFA)-based optical amplification. Benefiting from improved OSNR, the frequency stability was increased by more than one order of magnitude below 1000 s averaging time, and the phase noise was reduced to the noise floor below 0.1 Hz offset frequency. The proposed optical signal amplification approach has a potential application for transferring atomic clocks over long-haul fiber links.