A new tableau-based calculus for first-order intuitionistic logic is proposed. The calculus is obtained from the tableau calculus for classical logic by extending its rules by A-terms. Aterms are seen as compact representation of natural deduction proofs. The benefits from that approach are two-fold. First, proof search methods known for classical logic can be adopted: Run-time-Skolemization and unification. In contrast to the conventional tableau, sequent, or natural deduction calculus for intuitionistic logic we get no problem with order dependance of rule applications in our calculus. Therefore, backtracking is only necessary in the selection of unifiers. Second, as a by-product A-terms are synthesiszed for free during proof search. A-terms are important, when intuitionistic logic is applied in a program synthesis framework. We implemented the calculus in Prolog. A strategy which is similar to model elimination has been built in. Several formulas (including program synthesis problems) have been proven automatically.