The main objective of this work is to explore the theoretical existence of traversable wormholes in Rastall teleparallel theory under the matter source described by solitonic quantum wave and Navarro-Frenk-White density profiles. We utilize the Morris-Thorne geometric setup to describe the wormhole geometry, from which the anisotropic field equations are obtained in terms of the torsion scalar. Under a constant redshift function, we derive the shape functions in connection with both dark matter