You can download Treaties in Force: A List of Treaties and Other International Agreements of the United States in Force on January 1, 2013 from the State Department website. (They haven't published it the last couple years due to IT issues, apparently.)

Your treaty is not in the list. There is a treaty of amity with the UK from 1794, which is the oldest treaty that I was able to find except for the peace treaty from 1783. (Tip: Search for ", yyyy" to look for a year and avoid finding serial numbers.)