This link takes you to the top level page at the Library and Archives Canada dealing with records from the War of 1812. To get to the database to do a search, click the link on the left side of the landing page titled "Search" Database." But before you do that, scroll down the page to the section titled "The Database" to see what records are there, and how to use the search tools.
These are Canadian records, of course. But remember that some of those Canadians were loyalists that left the United States after the Revolutionary War. So you are liable to find Canadians and Ex-US citizens both in this database.
War of 1812 - Library and Archives Canada:
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