No. His lineage traces back to Elrond's brother. Elrond and his brother (whose name I've forgotten) were both half elf and half human, with the ability to essentially choose which side to embrace. Elrond chose to be an elf, his brother chose human.

He then founded the kingdom of Numenor, which was an island nation off the west coast of Middle Earth. It eventually (a few hundred years later) got destroyed by the sea/God and the surviving Numenorians set up the kingdoms of Gondor and Arnor in Middle Earth.

That was many, many years before Aragorn. So there's a tiny, tiny, tiny percentage of elf in there, which is why Numenorians live a bit longer than normal humans and are usually taller, but it's not enough to say he's Elven.