We propose tensorKanren, a relational programming language where each relation expression denotes a tensor. We formalize a type system that restricts the tensors to finite size. We then define a semantics that is parameterized by the semiring that the tensors draw their elements from. We compile tensorKanren types to bitstring representations. For the Boolean semiring, this compilation enables us to use an SAT solver to run tensorKanren programs efficiently. We compare the performance of tensorKanren and faster miniKanren for solving Sudoku puzzles. Our experiment shows that tensorKanren can be a more efficient variant of miniKanren.