No, he's a Dúnadan. That's a group of humans who were allied with elves in the distant past, and elvishness sort of rubbed on to them in some hand-wavey way. It's actually pretty damn rare for humans and elves to pair up on Middle-Earth, since this means that the elf permanently loses their immortality. I think there's only two or three examples of that happening in Tolkien's works. Beren and Luthien & Aragorn and Arwen come to mind.
The third you are looking for is Idril and Tuor, who were the parents of E?randil, who was the father of Elrond. E?rendil wife, Elwing, were herself quater human (grand child of Beren and Luthien), so their children Elrond and Elros were considered half elves. Elrond chose the life of an immortal elf, whereas Elros chose the life of a mortal man, and became the first king of Numenore. As the Dunadain are the survivors of Numenore, it is implied that Aragon is the distant decendent of Elros (I do not remember the family tree that well), and has some elven blood in him. Even if it has been "watered" down over many, many generations.