This study examines the vibration characteristics of static drill-rooted nodular (SDRN) piles in elastic soils under time-harmonic torsional loads via an analytical approach. SDRN piles, which are characterized by uniformly distributed nodes and enhanced surrounding cemented soil, are able to increase the vertical bearing capacity in soft soils. Piles are modelled using elastic rod theory, while surrounding soils are separated into two sublayers along radial direction: a core zone made up of cemented soil and an outer semi-infinite natural soil layer. An analytical method is proposed to solve the problem after formulating the wave equations for pile and radial soil layer. This methodology rigorously considers the continuity of twist angle and shear stress across the interface of the pile and radial soil layers. The simulation of nodes in the SDRN pile involves discretizing the pile-soil system and applying the principle of impedance function recursion to accurately compute the torsional stiffness at the top of the pile. Developed results are validated against the existing benchmarks for a cylindrical pile in elastic soil. Detailed numerical examples are carried out to assess the effect of major factors on the torsional impedance of the pile. For improved comprehension in engineering applications, the impedance function is applied to derive the twist angle of the rigid foundation, with the amplitudefrequency response expressed in a closed form. Results indicate that the vibration behavior of the piles is significantly influenced by the inner radius, outer radius, the dimension of the node, the radial width of the cemented soil and the damping ratio of the radial soil layer. The developed solution offers valuable insights for the optimization design of SDRN piles under dynamic torsional loads.