The streaming instability (SI) is one of the key mechanism to form km-sized planetesimals from dust grains or pebbles, which is a critical step in the standard core accretion scenario of planet formation. By enhancing the local dust-to-gas ratio to the point of gravitational collapse, the SI can overcome the collisional and radial drift barriers to grain growth. Recent study finds that there is a new form of SI driven by the azimuthal velocity difference between dust and gas, which results from the gas undergoing accretion due to magnetic torques. This azimuthal-drift SI (AdSI) can remain effective even without a radial pressure gradient, unlike the classical SI. In this work, we extend previous simulations of the AdSI by carrying out a large parameter survey. We investigate how the dust and gas evolutions vary with dust-to-gas ratios and grain sizes. We place focus on the low dust-to-gas ratio regime, where the classical SI is weak, but the AdSI is still effective, to study whether or not the AdSI can facilitate planetesimal formation in dust-poor environments.