This paper presents an integrated optical signal processor (OSP) design using CMOS-compatible silicon photonics technology, offering a tunable RF bandpass filter (5G/6G frequency range) with a programmable bandwidth and symmetric out-of-band rejection. The OSP is comprised of two identical microring resonators cascaded with a common bus waveguide, in 220 nm silicon-on-insulator substrate. The ring resonators are designed with low-loss rib waveguide structures (supporting fundamental and first-order TE-like modes) to ensure relatively lower propagation losses and to obtain high-Q resonances. The single-mode bus waveguide is designed to facilitate the desired range of coupling strengths via thermo-optic tuning. Four thermo-optic phase shifters are integrated to tune the resonant wavelengths and the Q-values of the individual microring resonators. The four phase shifters could be programmed to obtain desired optical filter characteristics of the fabricated OSP chip. The RF filter experiments were carried out using an off-chip laser source (λ ~ 1550 nm), a phase modulator (3-dB BW = 10 GHz) and a photodetector (3-dB BW = 26.5 GHz). The central frequency of the RF bandpass filter could be tuned upto 8 GHz in our experimental setup. The 3-dB (20-dB) bandwidth of the filter was tuned from 0.84 GHz (2.77 GHz) to 1.8 GHz (5.47 GHz) with a symmetric out-of-band rejection > 20 dB (above noise level). Even though the fabricated OSP chip has the potential to realize filter response beyond 50 GHz, the observed tuning range is limited by the efficiency of the thermo-optic phase-shifters, and the bandwidth of phase modulator/photodetector used in our experiments.