Few historians would say so, I think. History uses different methods and produces different kinds of knowledge. It's an established enough discipline that there's not the kind of need to self-justify you used to see (and sometimes still do) in other social sciences trying to co-opt the authority of science via similar jargon and claims.
That said, two points: First, there are no real solid demarcations for what is and isn't science, and you could make a reasonable case to include history if you wanted to, it just wouldn't be how very many people out there think of history. Second, science is sometimes a useful analogy for historical research, because both enterprises are about trying to answer questions by going and finding as much data as possible, then interpreting it in as convincing of a manner as possible, and trying to get everyone else in the field to believe you and think your work is interesting. Neither science nor history matters in a vacuum.
No, historians are not scientists.
Take the study of historical demography, for instance. This should be as scientific a field as possible - population statistics are all quantitative, and it should be as simple as measuring the population size, mortality rate, fertility rate and net migration rate. These vital events also tend to be well-recorded, so you can have reasonable confidence that your figures will stand up to heavy statistical analysis.
The Princeton Group aimed to use demographic history scientifically - that is, they hoped that by studying what caused the fertility decline in Europe they could come up with ways to reduce fertility rates in the developing world, which would help these areas grow economically because adults would have fewer children to support.
The Princeton group, led by Ansley Coale, spent the 1970s studying European countries' demographic experiences, trying to compare between countries and between areas within countries to assess the role of various factors - urbanisation, wages, female employment, class structures, availability of property and so on. They came together at a conference in 1979, and came up with confusing conclusions; whilst many were willing to advance particular factors for individual countries, no general theory was produced. For one of the most scientifically-minded historical projects, the result of years of collaboration was a great deal of new insight and information but no definitive conclusions - it's a great example of how we need evidence to write history but the evidence alone is insufficient to produce a convincing explanation.
Another example is proto-industrialisation theory. This theory argues that industrialisation was preceded by the growth of rural industry (mostly textiles and small manufacturing like making tools). Rural industry provided cheap labour, as agriculture leaves farmers without work during some seasons. The theory states that proto-industrialisation established greater markets, credit networks and encouraged smallholders to become full-time wage labourers. Theoretically, proto-industry would then increase labour costs as increasing industrial productivity outpaced population growth and made labour more scarce, prompting merchants to spread market relations ever-deeper into the countryside until bureaucratic costs became so high that it was cheaper to concentrate workers into a factory where they could be supervised. Factories = industrialisation (at least in this theory), so this is how the causal link works.
This theory prompted a proliferation of regional studies to test the hypothesis after F.F. Mendels suggested it in the early 70s. Again, we get into the trap that you can always find an exception to whatever rule you invent - whilst for some areas high wages have been seen as key to facilitating industrialisation through proto-industrialisation, for the Netherlands the explanation is that high wages prevented industrialisation by preventing capital accumulation whilst Belgium's low wages permitted growth. Then there are also areas of proto-industry which de-industrialised like the Weald of Kent in England, which was a major textile and glass production centre in the 16th century but had collapsed by the 18th.
Then to add to all these exceptions and contradictory explanations you have the problems of a general theory - in the West Riding of Yorkshire in England, woollen farmer-weavers generally weaved wool from their own sheep with their own tools and sold to local merchants, whilst worsted (it's a type of cloth) farmer-weavers were typically employed by specific merchants. These merchants were often not local, and provided the materials for the weavers to weave.
These two examples both come from fields of history - demography and economic history - which should be most open to scientific analysis. However, in both cases a scientific approach provides us only with useful organising concepts rather than final solutions or even coherent arguments. Applying the scientific method struggles with the fact that it is impossible to control the other variables, and the variables are so many and interact with each other in such complex ways depending on what other conditions exist. I realise I've been a bit harsh on science in my answer (since it does not generally aim to provide definitive answers but instead the best explanatory model which may be revised), but these two examples provide an illustration of some of the pitfalls of a scientific approach. Both have been major contributions to historical knowledge and helped other historians think about the problems, but because they cannot produce a universally-applicable causal mechanism it cannot be said that treating history as science is adequate. Yes, there are some similarities in methods, but history has failed in its claims to be able to use its data for prediction or modelling - it can explain but it cannot predict.
For further reading on these examples, start with Andorka, Levine and Tilly's review of The Decline of Fertility in Europe by Coale et al for demographic history. For proto-industrialisation, the tiny booklet Proto-Industrialization - The First Phase of Industrialization? by L.A. Clarkson outlines some of the difficulties and can be read in an hour or two. For a more up-to-date take, Shelagh Ogilvie has edited a book of proto-industrialization.