PSR B1706−44 is an energetic gamma-ray pulsar located inside supernova remnant (SNR) G343.1−2.3 and it powers a compact pulsar wind nebula (PWN) that shows torus and jet structure in X-rays. We present a radio study of the PWN using Australia Telescope Compact Array observations at 3, 6, 13, and 21 cm. We found an overall arc-like morphology at 3 and 6 cm, and the “arc” shows two distinct peaks at 6 cm. The radio emission is faint inside the X-ray PWN and only brightens beyond that. We develop a thick torus model with Doppler boosting effect to explain the radio PWN structure. The model suggests a bulk flow speed of ∼0.2c, which could indicate significant deceleration of the flow from the X-ray emitting region. Our polarization result reveals a highly ordered toroidal B field in the PWN. Its origin is unclear given that the supernova reverse shock should have interacted with the PWN. At a larger scale, the 13 and 21 cm radio images detected a semicircular rim and an east-west ridge of G343.1−2.3. We argue that the latter could possibly be a pulsar tail rather than a filament of the SNR, as supported by the flat radio spectrum and the alignment between the magnetic field and its elongation.