No, actually, he wasn't. His political rival John Quincy Adams and JQA's supporters formed the Whig party from several smaller parties like the National Republicans, the Free Soil party, a Libertarian party (unrelated to the Libertarians of today), and some other smaller groups.
This Whig party was formed solely in opposition to Jackson. It was Jackson's supporters who formed the Democratic party around him in response to the Whig party. So, it's not accurate to say he was a Democrat.
Before his run for the Presidency, there were multiple small parties. He was such a polarizing figure that he is responsible for the 2 party system we're stuck with to this day.
I could go on about how terrible he was as a President and a person. He was a truly vile man.