Um, no. I wouldn’t think so. I don’t see him as vampire-like. The Ringwraiths, on the other hand, the Nazgul. THEY are vampire-like. The Army of the Dead, too, from the third book and movie. But the Lord of the Rings himself?
Much hay is made by the author of this linked article of Tolkien mentioning vampires in THE HOBBIT and his other writings. Here’s an actual passage from the former: “Soon actual darkness was coming into a stormy sky; while still the great bats swirled about the heads and ears of elves and men, or fastened vampire-like on the stricken.” It would seem, if anything, that Tolkien here is talking about vampire BATS, which the author concedes. But more on that in a second. Here’s a better example, taken from THE SILMARILLION: “She was the messenger of Sauron, and was wont to fly in vampire’s form to Angband; and her great fingered wings were barbed at each joint’s end with an iron claw.” We will concede that vampires exist in Middle Earth, then. (Was it ever up for debate, though? Is anybody arguing the fact with this lady? She alludes to a “Tweetstorm for which I got all the internet fury…” but the tweet in question was actually about THE LOST BOYS and how they aren’t really vampires.)
Where’s the foundation of the argument that Sauron was a vampire? Per the author: “Tolkien’s version of a vampire…[is] not a shambling corpse fresh out of the ground searching for blood [but] a giant, intelligent bat…” Ah. Okay, then. She’s right. Sauron did at one point turn himself into a vampire. A vampire akin to the sort found in VIKRAM AND THE VAMPIRE as opposed to, oh, I don’t know, THE LOST BOYS.