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Yes, you can sue him in Arizona if that is where they are headquartered in the United States. The US would have personal jurisdiction over them in this instance.
Two issues that you need to be aware of though.
First, does the contract have a forum selection clause (saying something like that any disputes have to be brought in a specific court). If there is such a clause, you would most likely have to bring the case in that court.
Second, even if the contract does not have a forum selection clause, after you bring the lawsuit, the broker could file a motion for the case to be dropped due to improper venue. If the contract was signed in Mexico and dealt with goods that are centered in Mexico, then the broker could say that the proper venue for this case should be in Mexico. This could potentially be a losing argument for you based on the facts as you stated them.
Unfortunately, this clause could be enforced if the broker wanted it to be. You could try to bring the suit in Arizona, and maybe the other party will not challenge it because he would rather litigate in Arizona rather than Mexico. But if he raises the issue that the case has to be brought in Mexico, then it would most likely be dismissed in Arizona.