Well, you have to be careful with this stuff. It's exemplified well by what I turn up if I Google 'viking amulet'. The internet is happy to tell me all about (and sell me) all sorts of stuff. Most of what's in those search results is just free fantasy vaguely riffing on Viking Age Scandiavian (and Celtic) art. A bit disturbingly there's also the 'black sun' of the Nazi SS in there (second image in reading order). Very common are also the 'Vegvísir' and 'Ægishjálmr' magical symbols (first and third), taken from a couple of 17th century (or thereabouts) Icelandic grimoires (magic books) and passed off as being Norse and Pagan simply because they were from Iceland, ignoring the fact that similar symbols had been appearing in grimoires across West Europe for around a century by that time. (e.g. 1, 2, 3, 4, 5) In other words, European Early Modern magic, not Norse folklore. (Depressingly, they're popular as tattoos among people who've bought into the misconception) Then there's a smaller number of ones that are replicas of or at least based on actual Viking Age artifacts. So this is pretty representative of the situation outside of academic scholarship: Lots of well-intentioned but bad information going around, romanticism and exaggeration, neo-paganism and even racism. And tons of misconceptions.

The biggest misconception is that we know a lot about Old Norse Religion. We don't. The preserved written accounts are either from Iceland, centuries later, written in large part by Snorri. Or they're from contemporary non-primary accounts like Adam of Bremen, and are exaggerated. They all have at least some Christian biases. There are zero written sources from actual Viking Age Scandinavians, other than inscriptions, and most of those are formulaic and say little. We know a lot about what's written, we know relatively little about what it has to do with what was actually practiced. The other big myth is that Old Norse Religion was some unchanging monolith of 'pure' Germanic-ness, practiced the same by all Scandinavians until Christianity came along and some sort of 'clean break' was made because once christened, people had no tolerance for the old ways . This is entirely false, things changed about the religion over time, different practices were common in different places, there was syncretism going on during the Viking Age and just after it, and Roman influences long before it. (including the Runic alphabet) And practices that didn't directly contradict Christianity continued to a large extent.

So what can we say about amulets from the no-nonsense point of view? That means looking at the archaeological record. And there, we have plenty of evidence of various things thought to be amulest. Such as axe-shaped pendants, finger-rings and ring necklaces.

One thing that seems to have caught on in the 9th and 10th centuries was Thor's hammer. As a pendant on hammer necklaces and the very often reproduced hammer from Erikstorp. The viking-romantics were quick to declare this as a counter-reaction to Christianity, but since hammers have been found in the same graves as Christian cross pendants, it's uncertain the users really saw a contradiction there.

God figures exist too; Odin from Lejre in Denmark and Freya from Aska and Freyr from Rällinge. Whether it's actually those gods in these and many other cases is somewhat disputed though. E.g. almost every book about Norse Mythology will tell you that's Freyr, making it seem quite certain, but it's only the fact that he's sporting an erection that lead people to conclude it's the fertility god.

Both men and women made use of amulets and some forms were very widespread. It's far more difficult to know what their ritual purpose was, and whether any amulets were considered particular for fighting. Similarly if a charm was unique to a person, there's really no way of knowing that it even was a charm. One might compare to medieval sword inscriptions, which we at least know were intended to confer some magical charm or prayer, but are often undeciphered (e.g. "NDXOXCHWDRGHDXORVI") because the inscription didn't need to make sense to anyone other than the user. In an illiterate society, letters and words were sometimes considered to be inherently magical, too. That was also exaggerated in the case of Norse runes, which are now considered to be either non-magical in themselves ore at least much-less magical than previously thought. For instance, some inscriptions that in the past had been interpreted as ritualistic magical repetition of a particular rune, are now thought to have just been someone learning to write.

Anyway, a runestone would be too big and heavy to carry around, those were usually monuments of various kinds. There are however inscriptions on wood, bone and, in the late Viking Age and early Scandinavian Middle Ages in particular, metal plates. Out of the later ones, many are related to contemporary christian folk-magic from the continent, such as invocations of Saint Michael. Michael is often depicted as a warrior, but otherwise there is little in the way of explicit magic charms to help warriors.

One exception might be the Hávamál (verse 158) which has a curious warrior blessing in the Ljóðatal, a set of magical chants. The verse states that if one throws water on a thegn , he will not fall in battle, which might be a pre-christian allusion to baptism. (the protective powers of baptism was strongly ingrained with the Christians of the era)

Anyway, so the short of it all is that yes, Viking Age Scandinavians certainly had amulets, and certain types like Thor's hammers were quite popular, even if their use and purposes of the amulets in general rather murky, much like many many other practical aspects of the religion. if you want to go in-depth the book Runic Amulets and Magic Objects (2006) by MacLeod and Mees is a good overview of both the artifacts, runestones and sagas, and puts them in decent perspective, and I've used it a bit here.

Some other sources:

Erik Floderus, Brandgravar med hängkors , Fornvännen 129-133

Anders Andrén, Behind Heathendom: Archaeological Studies of Old Norse Religion, Scottish Archaeological Journal 27(2):105-138 · October 2005

Helmer Gustavson, Lära sig och lära ut runor – med hjälp av futharken? , Situne Dei 2013.

And the collections of the National Historic Museum in Stockholm.