We report on a mid-infrared mode-locked fiber laser that uses an acousto-optic tunable filter to achieve frequency-shifted feedback pulse generation with frequency tuning over a 215 nm range. The laser operates on the 3.5 ${\mu}$m transition in erbium-doped zirconium fluoride-based fiber and utilizes the dual-wavelength pumping scheme. Stable, self-starting mode-locking with a minimum pulse duration of 53 ps was measured using a two-photon absorption autocorrelator. The longest wavelength demonstrated was 3612 nm and a maximum average power of 208 mW was achieved. This is the longest wavelength rare-earth doped mode-locked fiber laser demonstrated to the best of the authors' knowledge. The broad tunability promises potential uses for environmental sensing applications.