Spinors play a fundamental role in geometry and physics. The Clifford algebra is the natural linear algebraic setting where spinors and spin groups are formulated. In this study, spinors, which have many uses in Clifford algebras, have been given with a different representation in E3. Firstly, the directional q -frame has been considered, and this frame is represented with a spinor in spinor space. Later, considering the relations between the directional q -frame and Frenet frame, the relations between spinors corresponding to these frames have been obtained. In this way, a different construction of the spinors by using in Clifford algebras has been shown.