There is no procedure. The US does not have a central repository of marriage or divorce records. Rather they are maintained at a state (or lower) level. As such, you would only need to "prove" your Algerian divorce in the US if you were asked to do so as part of a federal process here.
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However, a lot might depend where that former wife is now and if she recognizes the divorce. If the divorce was done without one or both of the parties that could be a problem if the other party does not recognize the divorce and is in the US.
This is not legal advice but a general comment on society. International Law 24/7 hotline +1-202-318-2406 - Dr. Jonathan Levy, PhD calls or emails usually returned within 24 hours.