In this paper, both trigonometric and rational solutions to the Yang-Baxter equation associated with the spinor representations of the quantum universal enveloping algebras are obtained. The quantum Clebsch-Gordan matrices, the quantum projectors and the solutions are the block matrices with the dimensions of the submatrices to be 1 and , where , if is even, , if is odd. The explicit forms of the submatrices with the same dimensions are independent of . As examples, we discuss the solutions for the spinor representations of the quantum to , and present the explicit forms of those submatrices with the dimensions 1, 2, 8 and 32. The corresponding representations of the braid group and the link polynomials are also computed through a standard method.