Yes, a Tiefling can be a Paladin (and Tieflings don't have to be evil)
In general, there is no restriction on any combination of race, class, and alignment in 5th Edition D&D. The very first editions of D&D did restrict Paladins to only being humans, but that restriction was abandoned by 3rd edition, and any race could take up the mantle of a Paladin. 3e and previous editions did also restrict Paladins to a single alignment - Lawful Good - but that doesn't preclude Tiefling Paladins (Tielfings can be Lawful Good despite their heritage, after all). In any event, even that restriction was dropped in 4e onwards, and in 5e the core Paladin class definitely has no restrictions on race or character alignment.
The actual description and flavour given for the class in the manuals does lean very strongly on appeals to goodness and virtue, which makes the idea of an Evil Paladin seem incongruous - this is quite deliberate, as D&D's explicitly preferred style is a story about virtuous heroes, not villains and monsters. However, no actual mechanical rule forbids a Paladin of Evil alignment.
It does get a bit more complicated when it comes to your choice of your Paladin's Sacred Oath and the tenets of those oaths. All of the Oaths available in the Player's Handbook have explicitly Good tenets that the Paladin must follow, and the "Breaking Your Oath" sidebar states:
A paladin tries to hold to the highest standards of conduct, but even the most virtuous paladin is fallible.
If a paladin willfully violates his or her oath and shows no sign of repentance, the consequences can be more serious. At the DM’s discretion, an impenitent paladin might be forced to abandon this class and adopt another, or perhaps to take the Oathbreaker paladin option that appears in the Dungeon Master’s Guide.
So it's clear that it's not really acceptable for a Paladin holding to these good oaths to be actively evil. It could be an interesting choice to play a character who is philosophically evil, yet for whatever reason has decided to adopt one of these Paladin oaths and be actively good; the disjunction between the way they feel compelled to act and their real feelings certainly sounds like delicious drama for the right kind of players.
If you want to be actively evil, though, you will need to look for different oaths - like the "Oathbreaker" variant from the DMG that is referenced here. Xanathar's Guide to Everything includes a couple of new Paladin Oaths also, one of which is the "Oath of Conquest", featuring tenets like:
- Douse the Flame of Hope
- Rule with an Iron Fist
- Strength Above All
So that's clearly a very good fit for a Lawful Evil Paladin, and nothing seems wrong about a Lawful Evil Tiefling Paladin following the Oath of Conquest. However, as with any character concept, you should probably make sure your DM (and your group) is on-board with the idea. Any other considerations aside, it might be that they don't really want to play a game with evil characters, and would rather stick to more traditional feel-good heroics.
Tieflings don't gotta be evil
Just in case this is a misconception on your part, I will point out that Tieflings are not inherently evil creatures:
Alignment. Tieflings might not have an innate tendency toward evil, but many of them end up there. Evil or not, an independent nature inclines many tieflings toward a chaotic alignment.
The standard fluff suggests that the curse placed upon their bloodline happened far enough back in the ancestry that though their physical appearance is obviously drastically affected, it does not directly influence their morality or actions. So, there's no inherent reason a Tiefling Paladin should be unusual. It's the matter of whether a Paladin can really be evil that is the real issue.