Marco Polo's Travels calls them unicorns, but notes that they are very different from the European unicorn:

There are wild elephants in the country, and numerous unicorns, which are very nearly as big. They have hair like that of a buffalo, feet like those of an elephant, and a horn in the middle of the forehead, which is black and very thick. They do no mischief, however, with the horn, but with the tongue alone; for this is covered all over with long and strong prickles [and when savage with any one they crush him under their knees and then rasp him with their tongue]. The head resembles that of a wild boar, and they carry it ever bent towards the ground. They delight much to abide in mire and mud. 'Tis a passing ugly beast to look upon, and is not in the least like that which our stories tell of as being caught in the lap of a virgin; in fact, 'tis altogether different from what we fancied.

But the European unicorn appears to have its origins in the rhinoceros, so the discovery of the rhinoceros predates the standard horse-like unicorn of European beast-lore. The oldest known literary unicorn is that of Ctesias, in his 5th century BC book Indika, in which he describes things of India. His unicorn is described as a horned wild ass:

India has wild asses as large as horses, with a purple head, blue eyes, and a white body; they have a horn on the forehead a cubit long, the lower part of which, or that nearest to the skull, is very white, whilst the middle is black, and the tip red ... The Indian wild ass is a very strong and swift animal; no other can overtake it. At first it runs gently, but it increases its velocity as it proceeds. It is captured only by this device: - when droves of them take out their young to pasture, they are surrounded by horsemen, and being unwilling to abandon their young, they do not gallop off, but remain and fight with horns, heels, and teeth, and kill many of their assailants: at last, however, they are overpowered and slain with arrows and darts; they are never taken alive.

Aelian, writing some 6 centuries later, quotes Ctesias, and adds that the animal is sometimes called a "kartazonos" (καρτάζωνος). This appears to come from the Persian name for the rhinoceros, kargadan or kargazan. A more detailed, and more rhino-like description is given by Pliny the Elder (also following Ctesias):

in India ... the fiercest animal is the unicorn, which in the rest of the body resembles a horse, but in the head a stag, in the feet an elephant, and in the tail a boar, and has a deep bellow, and a single black horn three feet long projecting from the middle of the forehead. They say that it is impossible to capture this animal alive. (Natural History, 8,31).

Pliny also describes the rhinoceros:

At the same games there was also a rhinoceros with one horn on the nose such as has often been seen. Another bred here to fight matches with an elephant gets ready for battle by filing its horns on rocks, and in the encounter goes specially for the belly, which it knows to be softer. It equals an elephant in length, but its legs are much shorter, and it is the colour of box-wood. (8,29)

and

No species has both solid hooves and two horns; the only animal with one horn is the rhinoceros, and the only one with one horn and cloven hooves the antelope. The rhinoceros is the only solid-hooved animal that has pastern-bones (11,106)

which tells us that the unicorn had assumed a life of its own, separate from the rhinoceros, and that Pliny didn't identify the rhinoceros as a unicorn (unlike Marco Polo).

References:

Marco Polo, Travels: https://en.wikisource.org/wiki/The_Travels_of_Marco_Polo/Book_3/Chapter_9

Pliny the Elder, Natural History: https://en.wikisource.org/wiki/Natural_History_(Rackham,Jones,%26_Eichholz)

H. H. Wilson, Notes on the Indica of Ctesias, The Ashmolean Society, 1836.