A* is an extension of Dijkstra's algorithm where the optimal solution of traversing a directional graph is taken into account. I'm not sure this applies to the TSP problem.
The TSP problem states that you want to minimize the traveling distance while visiting each destination exactly once. The A* algorithm needs a heuristic to guide it's way where the optimal solution is known to be a straight line (you have to be careful with the A* heuristic to not overestimate the distance to the goal). This dose not apply to the TSP problem.
This question also contains information about the A* algorithm and TSP problem.
