Given any associative k-algebra A, the Ext algebra is a graded k-vector space with algebra structure given by the Yoneda product. The Ext algebra served as an important homological invariant for various reasons. Moreover, it is known that taking the Ext algebra is a process that distributes nicely across tensor product, i.e. Ext(A ⊗B)≅Ext(A) ⊗Ext(B). Therefore it is natural to ask if the same statement holds for the non-commutative analogue of tensor product, twisted tensor product.