Biology student with a lifelong passion for history here (many years ago I wrote an essay about the history of the indian rhino in european culture and art).

Short answer: No

Let's get into the Dürer rhino before I shortly discuss why its heavenly unlikely that rhinos where ever used as war animals.

The animal depicted by Dürer was a gift to the king of Portugal and he only knew of it from an letter which was sent to Nuremberg by an portuguese merchant. Unfortunately this letter didn't survive but it is most likely that it contain vivid description (comparing it with a knight's armour) and a drawing. If you compare Dürer's woodcut with a real indian rhino it's amazing how lifelike his beast really is. To this day the indian rhino is called Panzernashorn (armoured rhino) in the German language because it skin really looks like the plates of a knight's armour.

The really outrageous part of Dürer's rhino is the German text which vividly paints a picture of a beast as big as an elephant that is a merciless killing machine running under every elephant's stomach to rip it apart with its horn.

„Nach Choistiegeburt/1513. Iar Adi 1. May. Hat man dem großmechtigisten König Emanuel von Portugal/gen Lysabona aus India pracht/ain solch lebendig Thier. das nennen sie Rhinocerus/Das ist hie mit aller seiner gestalt Abconterfect. Es hat ein Farb wie ein gepsreckelte Schildkrot/und ist von dicken Schalen uberleget sehr fest/und ist in der größ als der Heilffandt/Aber niderichtervon baynen und sehr wehrhafftig. Es hat ein scharffstarck Horn vorn auff der Nassen/das begundt es zu wetzen wo es bey staynen ist/das da ein Sieg Thir ist/des Heilffandten Todtfeyndt. Der Heilffandt fürchts fast ubel/den wo es Ihn ankompt/so laufft Ihm das Thir mit dem kopff zwischen die fordern bayn/und reist dem Heilffanten unten am bauch auff/und er würget [erwürgt?] ihn/des mag er sich nicht erwehren.dann das Thier ist also gewapnet/das ihm der Ieilffandt nichts Thun kan/Sie sagen auch/das der Rhinocerus/Schnell/fraytig /und auch Lustig/sey.“

"AD 1513. 1st May. Such a living animal was brought the mighty king Emanuel of Portugal from India to Lisboa. They call it Rhinocerus. This is shown here with all his shape. It has the color of a sprinkled tortoise and is covered in thick firm shells and is about the size of an elephant. But has smaller legs and is very belligerent. It has a sharp horn at the top of its nose which it grinds whenever it is near rocks. It is an victorious animal and the mortal enemy of the elephant. The elephant is scared to death of it, because whenever it sees it (the elephant) it runs with its head underneath the elephants leg and tears the elephant's stomach open. Than it chokes it and the elephant can't defend itself because this animal is so armoured that the elephant can't harm it. They also say that the Rhinocerus is fast, wild and cunning."

Although the story of the Elephant vs. Rhinoceros fight is as old as the Natural History of Plinius. (And there are accounts that king Manuel tested this account and neither animal killed the other one). There is one and just one reason why this text was on Dürer's woodcut - and this is the same reason why the text is in German and not in latin: It's the equivalent of a false TIL headline to gain upvotes) You see there was no internet and all the stories of deformities, curioisites and strange goat-human hybrids were distributed with woodcuts. Everytime someone bought a woodcut with the story of the strange killing monster from India Dürer made money. This sells better than "there is a new animal in the menagerie of the king of Portugal. It eats grass and is slightly bigger than a large cow."

That covers the Dürer rhino. Back to war animals. There is one common thing most animals used in war share. Trainabillity. Except big cats the former war animals are the same species you will most likely see in a circus today.

Dogs: domesticated for ca. 15.000 years. They see humans as part as part of their pack, are highly protective and easy to train. They breed good. They're the best animals for war.

Horses: domesticated for about 4000 years. We named cars after things that horses dragged around. They are the precar-car. It's a great advance in mobilization and fast flank maneuvres.

Elephants: Never domesticated. Has to be caught and trained. Very smart but high unpredictibility (the so called Musth in male asian elephants). Useful as a bulldozer, element of fear and moving archery tower. But once it breaks loose it will not distinguish between enemy lines and your own.

Rhinoceros: Never domesticated. Not very trainable. Short sighted. Easily scared. In fact it would be like using war bulls. And as a last thought of me let's look at this (very generous) map of distribution of rhino species: https://bookofbeasts.files.wordpress.com/2012/08/rhinoceros-distribution.png It does not really overlapp with the borders of the classic great empires.

According to this article, it seems the answer is no. Which makes sense, given the general behavior of rhinos is territorial and mostly solitary. These don't lend themselves to being tamed.