It seems to me that the War of 1812 is collecting more and more interest from genealogists. At least, I get more and more questions about it, especially in our class of military records.
If that is an area of interest for you, did you know that Ancestry.com has a database of transcriptions from that war?
When the United States declared war on Great Britain in 1812, Congress authorized the President to accept and organize volunteers in order to win the war. The database on Ancestry.com is a listing of men mustered into the armed forces between 1812 and 1815. Taken from records in the National Archives, each record includes the soldier's name, company, rank at time of induction, rank at time of discharge, and other helpful information. It provides the names of nearly 600,000 men.
There are no digitized documents to see, but the appearance of your ancestor's name in this database tells you that he did in fact serve and that his records are available.