The object of the present paper is to study 3-dimensional β- Kenmotsu manifolds whose metric is Ricci soliton with respect to Schouten- van Kampen connection. We found the condition for the Ricci soliton structure to be invariant under Schouten-van Kampen connection. We have also showed that the Ricci soliton structure with respect to usual Levi-Civita connection transforms to a η-Ricci soliton structure under D-homothetic deformation. Finally we have shown that if a 3-dimensional β-Kenmotsu manifold admits a Ricci soliton structure with respect to Schouten-van Kampen connection and potential vector field as the Reeb vector field, then the manifold becomes K -contact Einstein.